Here are pros and cons for longbows and composite (recurve) bows. Just read the Italics if you don't want to go thru the explainations. Many of the stuff I mention here are from reading the Bowyer's Bible, reading archery stuff and other people's posts, and I once visited a Korean archery range. I will assume that the longbow is a non composite, non recurved classic English wood longbow (therefore, not the composite longbow like the Japanese Yumi), and the composite bow is a recurve composite bow of horn and sinew, like the Korean bow (I couldn’t find too much info about piercing tests or performance tests about Chinese or Mongolian bows. Chinese and Mongolian bows also composite recurves and Mongols did do a pretty good job against heavily armoured Polish Knights.).
LONGBOW when compared to COMPOSITE RECURVE BOWSPros-
it is easier to find material to make the longbow than a composite bow. The best longbow used expensive yew, but any other wood could be used. Composites required the bowyer to find wood, glue, horn, sinew etc.
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It is cheaper to make than the composite bow- Longbow is made of only wood, so it is affordable, even to the peasantry. Horn or sinew used for composite bows on the other hand, are reserved for richer people and therefore, limited in numbers.
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it is easier and faster to make; Longbows don't take long to make, as the bowyer just needs to cut the bow out of (preferrably seasoned) wood. But composite bows require the bowyer to season the wood, cut the wood, cut the horn, make the glue, dry the glue, etc. Any mistake in a step will make a useless bow.
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anyone can afford it or make longbows. Because longbows are cheap and easy to make, large armies of longbowmen can be made in a quick time.
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It is serviceable even in wet weather. (the glue on Composite recurve bows cease to function in wet weathers, making the sinew comes off, making the bows unserviceable. Asiatic archers using these bows often had elaborate ways to keep their bows dry. In Korea, bows were kept warm in a heating box to keep out moisture, when unused.)
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This is purely my opinion, but the Mediterranean draw (2-3 finger draw) seems to be more accurate than the Mongolian (thumb draw) when shooting on foot. To aim with the Mediterranean draw, I look down the arrow shaft when it is drawn, and see if it points towards the target, and I intuitively guess by how much I have to raise or lower the bow. But with a Mongolian draw, you have to intuitively guess both the vertical and the horizontal aim since the end of the arrow rests behind my ear at a full draw. Some say that old longbow archers drew their arrow past their ears, in which case then, Mediterranean draw of the longbow is as hard as the Mongolian draw.
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Longbows draw easier in the beginning of the draw because of the design than the recurve. (This might be more of a con though)
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Longbows are disposable. Many Asian countries (I know Korea and Japan do) treat the bow as a living being, that deserves treatment equal to a human. No one should touch another man’s bow because she is like your wife, you have to keep it warm, you have to sing to it at night, blah blah blah…. This is because one has to go to so much trouble to get another bow if it is broken. You don’t have to worry about treating your longbow nicely, because you can always make another one. It is designed for rough, hard combat.
Cons-
Longbows, can't be sinewed to increase performance. If they are sinewed (and therefore become a composite longbow) it will perform worse than when it is not sinewed. For longbows, sinew only slows down the limbs when shooting. Longbows are sometimes backed with sinew, NOT to increase poundage, but to prevent the wood from splintering and the bow breaking. Sinew only works well on a recurve bow. To increase longbow performance through sinew, you have to recurve it (longbow design only allows for it a slight recurve.) , in which case, it is a recurve, composite longbow (If you recurve the longbow by a lot, )
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longbows can't be recurved as much as Asiatic bows because the limbs are thick. Longbows can have thinner limbs, but these are now flatbows of north American style. Big Asiatic bows, which were proportionately bigger and stronger than bows the shorter recurve, composite design were made in the past for ceremonial purposes and to power siegebows. These bows, I suppose can be considered recurved, composite longbows. However, these bows would not be practical for use of a soldier because it was so heavy to draw. One could create a recurve, composite longbow of a lower drawable poundage of 120 pounds, but these would perform less than a smaller 120pound composite, recurve, shortbow, because longer limbs= more limb mass= slower cast of the arrow because energy is lost in propelling the heavy arms forward.
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Longbow, because of its design, stacks poundage suddenly feels high when pulled far). This creates a harder pull. Composite recurves do not usually stack because of their design.
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Longbow's push of the arrows becomes weaker as the arrow leaves the string from a full draw. Recurved composites have their limbs curved away from the archer when unstrung. So, when strung, the bow is already under higher tention than a longbow. So, early in the draw stage for a recurve compositb bow, the bow limb is already of high poundage. Therefore, when an arrow is released, a composit recurve will push the arrow almost uniformly until the arrow leaves the string, whereas a longbow will push the arrow weaker and weaker as the arrow leaves the string.
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Longbows are big so they can't be used on a horse as efficiently as a shorter composit recurve. You can still shoot a longbow from a horse, but some horse archery techinques, such as the parthian shot and right side shot will be very hard. Composite recurve bows can easily be used on both foot and on horse. As well, two finger draw for the longbow would increase the chance of the arrows falling off the bow in a draw when shooting from a running horse (I think that is why, master horsearcher, Lajoss Kassai who uses a Mediterranean draw releases the arrow as soon as it is drawn, not only to shoot as quickly as possible, but because the arrow would fall off if he kept a drawn position on a horse too long, with a Mediterranean draw).
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Longbows are susceptible to wet weather as well. It won’t break down as badly as a composit recurve, but it will lose poundage, because the wood stays bent. But one can always make a new one

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Longbows require higher poundage to give out similar performance as composite recurves. Higher poundage = harder to draw, which in turn might decrease accuracy. As well, archers using composite recurves, because they had bows of lower poundage, didn’t have deformations in the shoulders like the longbowmen. (I never heard of any cases in Asiatic archers, but maybe because it is just not well known. However, I noticed that many Korean traditional archers had a deformed thumb, because they use the thumb release)
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Longbows could potentially have more handshock because sometimes (depends on design) the handle works in bending too.
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Longbows, contrary to popular belief, can’t pierce steel armour well. Tests done with reproductions of weapons and armour from Agincourt times (
http://www.youtube.com/watch?v=KyIk6XvGMTM&feature=related ://http://www.youtube.com/watch?v=KyIk...eature=related ://http://www.youtube.com/watch?v=KyIk...eature=related ://http://www.youtube.com/watch?v=KyIk...eature=related ://http://www.youtube.com/watch?v=KyIk...eature=related at 3:22min) proved that the soft iron arrows couldn’t pierce steel French armor at a distance (maybe results would be different if the arrow tips were steel). However, they were good at maiming horses, piercing chainmail, piercing unprotected parts, piercing steel armour at very close range (20m) etc. In Korea archery was so deadly in piercing metal armour, that soldiers started wearing leather, or layered cloth armour which gave more protection against arrows, or didn’t bother wearing any armour at all (much like gun combat). In Korea and some Arab, Turkish countries where they used composite recurves, there were special methods of shooting (pyunjun in korea) to shoot armour piercing, fast, long going small arrows. (see
http://www.youtube.com/watch?v=zJELZ0vYvV8...feature=related at 7:28) test was on a metal plate at 145m with 40-60? pound bow, but I’m not sure if it is as strong as French armour.
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Longbows don't have as great a flight distance as composite recurves. Longbows can achieve a flight distance of around 300m with a 110 pound bow, But composite recurves such as the Korean bow could reach 300m in flight distance with a 40-60 pound bow. (longbow arrows might be slightly heavier than Korean ones)
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Longer limbs make limbs heavy and slow when casting. But the design makes the most out of the wood they are made from.
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Narrow limbs of longbows easily take set (stay bent after bent) and break easily, although it gives more power and make efficient use of the wood it is made from.
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On a lighter note, Longbows can't be concealed (unless made very small lol, but it won’t be too leathal). One King of Korea wanted to kill his son, so he hid a bow in his sleeves. I think Yi Seong-gye was the king.
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The Mediterranean draw allows for less pull than the Mongolian draw. I don’t know if this is true or not, but Korean traditional archers claim that the Mongolian draw allows for a draw that is at least one hand’s length more than the Mediterranean draw.
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Longbows don't last very long. Some people say that a Korean bow, although it will lose some poundage over use, may last a bit less than a generation (30 years) without breaking, if it is kept well. I can’t say if it’s an exaggeration or not, but the longbow’s got ease of manufacture to make up for its short lifespan. Longbows that are not backed live up to 1 or 2 years depending on the amount of use.
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String stoppers present in Asiatic recurve composite bows, won’t do much good to a longbow because it is too long for the design to work anyway. (I’m not sure how a string stopper exactly works, but what I understand, it increases performance and don’t work well with longbows. I might be wrong on this one).
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Longbows may require more training than the composite recurves, as muscles and deformities in skeletal structure is needed to draw the heavy bow more efficiently. But since anyone could use them England had large pool of deformed men to use the longbow anyway

. In England, the limiting factor would be the men who can wield a longbow, in Asiatic countries, the limiting factor would be the bow.
CONCLUSION
Performance wise, the composite recurve bow beats the longbow. It is much more efficient in terms of the speed, distance and piercing strength the arrow obtains for the same poundage as the longbow. Composite recurves are easier to draw and therefore more accurate because it can be of lower poundage but still carry the same amount of lethality. But in terms of ease of obtaining the bow, whether one makes it or buys it, the winner is the longbow. A longbow army would be relatively easy to make from scratch, given than one has the archers to use the longbow, whereas, a composite recurve bowman army would be hard to make, even if one has enough bowmen. In different situations, the worst type of bow can be the best of bows.
I have written about Korean, Turkish and longbows on this forum even though it's a Chinese history forum. I am really disappointed that there isn't as much knowledge nor artefacts on traditional Chinese bows of the Han dynasty. Most Chinese bows surviving today seem to be Manchurian or Mongolian, with very little traditional Chinese bows. I suppose Han dynasty is too long ago for any material to survive to this day, and Chinese bows probably adapted the styles of other bows through the ages. The site
http://www.atarn.org/ offer a lot on Chinese bows, and I encourage everyone interested to check it out. However even here, I can't really find a satisfying amount of articles on Han bows. Crossbows seem to be have been used predominantly in this dynasty and earlier dynasties but there was also a definite bow use in China as attested by bow manuals, records and paintings. Many ancient bow training manuals and folklore for bow wielding heroes can be found, but not many bows survive to this day. Much of China's ancient bow culture sadly, seems to have been extinguished. But from what I can gather, Chinese bows were of much variety, of recurved composite, to simple wood non recurved shortbow and adapted many styles.
Personally, I think, among the recurved composite bows, Korean and Turkish bows perform the best (and possibly Indian and Persian, but I have little knowledge of these bows to say anything about them). However, among all bows, I prefer the longbow, even though I know the merits of the recurve composite bow. I think I am enchanted by the romance associated with longbows (such as the battle of Agincourt, Robin Hood) although there are many interesting Asian folklore associated with the bow as well, such as Houyi of China, Jumong of Korea, Yatagarasu of Japan, Shiva and the bow of India. The truth is, there are many other bows that are better in performance than the longbow. The longbow however, with all its inefficiencies and ruggedness, will always remain to me, as the best bow.