That's silly isn't it? For U.S's case, Canada and Mexico can only put up so much pressure, yet does it imply anything of the power of U.S?
Power is not an absolute, but a relative thing: You are only as powerful as the counter-pressure of your neighbours and rival allow you to be, hence the most objective criteria of a powerful polity is the power of your rivals and how you fare against it.
It appears we have a different opinion of what is "China." Since majority of these 'foreign powers' do address themselves as 'China.' If you want to say culturally Han dynasty I would agree to some points.
Military: In this respect, I wouldn't place any Chinese dynasty even among the top twenty: for almost the larger part of the 2nd millennium AD, China was partly or fully occupied by foreign powers. And India, the other giant with feet of clay, was almost habitually overrun from Muslim intruders from its north-west.
Anyhow. Han dynasty under Han WuDi in the years of his expansion was basically unstoppable. During Tang XuanZhong's time, his force was also incredible powerful. During Zhu Di's time, I also don't see a rival.
On the other hand, if you are saying Chinese DYNASTY, then I fail to see ANY country been top [wait, isn't that contradictory?] given it must first rise, then fall, the mathematical laws DEMANDS it must cross the 0 threshold, thus, this point of Chinese dynasty is very very silly.
Did the British Empire remain most powerful throughout its history? No.
Did the Roman Empire? No.
Did any Empire? No.
I want source.
Economy: In terms of wealth, both had a GDP per capita not more than average in Asia, and below the European one most of the time.
Aside from current figures of GDP / capita, how in the name of heaven did you get GDP figures from Europeans? Now China do have a fair complete collection of census, income, grain/wheat prices, [w/out rubbishing your claim its less then European] but a comparison DEMANDS you provide the other set, now I would like to see the European average, please.
Also, if we are talking about the relative well being of the people, then perhaps GDP/Capita MIGHT be a key indicator. [Again, Cost of Living is FAR MORE important then GDP in well being, since it really is a show off piece of figures that have no meanings to average people.] but if we are talking about actual power, how is aggregate of economy NOT important? I would say its the most important thing.
Do you consider the average strength of an army? Or do you consider the aggregate strength of an army?
Perhaps the Spartans were stronger on average, but what does it mean if there are 2 Spartans and a gazillion Persians? [Unless, of course, the Expectation of both are the same.]
Wow. Just wow.
Cultural appeal: While Buddhism was a world force, Confucian culture was unconvincing in that only people of lesser cultural standing adopted it.
Normally I would just ignore something idiotic like this, but given a nation whose core value was Confucian, was able to survive through, your words, occupation by foreign powers over a great amount of time yet retain its cultural identity, while all those other culture which you shower your praise on [that is non-Confucian culture] all fall apart and hardly retain its identity, I find it extremely difficult to take most, if any of your statement seriously. At the same time, we also take note that Confucian teachings does not, unlike all other religion, give hope of salvation in the afterlife for good and eternal punishment in the afterlife for evil, and still millions follow its moral code, w/out the fear of divine reward/retribution, is something I would call, pretty darn good.