He agreed to serve Liu Bei mainly to stop Liu Bei pestering him for the fourth and N'th time. That, plus his two hooligan sworn brothers were beginning to be angry at him. And you can't really fight a Dragon crest sabre and a Snake tongue spear with a fan can you?
Jokes aside, rommantically, he served Liu Bei as he was touched by him. In the mordern world, imagine if the CEO of a company, albeit a smaller one, were to aproach you 3 times himself with 2 of his most senior colleagues in the firm - despite you not returning his calls.
He was also being promised to be heard, and his position as first advisor was pretty much on the cards.
Regarding that he chose Liu Bei just because he could fast-track his career instead of competing with others - I doubt it very much; picking Liu Bei who was fledging and didn't even have a steady base and not picking say, Sun Quan or Cao Cao whom both had vast influencial regions, money and military strength... can be pretty much termed as "career-dead" and not to mention a whole shitstorm of work to do by yourself.
Zhuge Liang under Cao Cao would indeed have fast-tracked Cao Cao's expansion for a couple of reasons - Sun Quan would not have stood against him at Chi Bi; Liu Bei would not have any one capable enough to advise him, and build up a capable stronghold to keep Cao Cao and his descendents busy. We probably see a Wei Dynasty instead of the Jin, and it could have been really quite good with the amount of talent Cao Cao had. Zhuge Liang's talent in military precaution in co-junction with the cunning and brilliance of Cao Cao's harem of strategist would steam roll Sun Quan's Zhou Yu. Zhuge Liangs extraordinary talent in administration would have helped Cao Cao's territories boom and her population be more content.