The more pertinent question is how Xiang Yu managed to lose. He had everything going for him and if he had simply kept Liu Bang bottled up in Hanzhong, nothing would have happened. In a sense, Liu Bang was simply too irrelevant to care about and so while every other feudal lord fought each other, the Han were allowed to bide their time.
A Xiang Yu victory will have massive consequences for China. It's easy to forget that Xiang Yu wasn't so much a founder of a new dynasty but the restorer of an old order. After all, Xiang Yu was Chu nobility, and what he wanted, first and foremost, was the reinstatement of the old order that the centralized Qin had swept away. This was something that wasn't present in the peasant-born Liu Bang.
Xiang Yu made a big point about re-splitting China into vassal kingdoms, ruled mainly by royalty/high officials of the previous order. now obviously this didn't mean that Xiang Yu himself was going to give up the supreme power (and anybody who challenged him would suffer the consequences), but he certainly was more lenient about the land division than Liu Bang, who largely nominated kings who were allies or former subordinates. I can't imagine that a Chu Dynasty would have the tendency towards political centralization that the Han Dynasty would have.
Long story short, Xiang Yu's comprehensive victory would probably have led to a re-establishment of Zhou-style feudalism in China, only this time with the center of power migrating away from the Guanzhong region to the Jiangnan region (Chu). Political re-centralization efforts would be half-hearted at best and eventually power would leak back towards the local regions, which over time would become economically and culturally divergent from each other.