The only reason I prefer Achievements is because every game for the 360 has them. I play a few games for the PS3 like MGS4 and Valkyria Chronicles that are great, but don't have trophies. Since I don't get credit for those games, I feel like my trophy level will never be a true representation of my accomplishments. Aside from that one little nitpick, they're just two different versions of the same thing.
-one other small gripe: Achievements add absolutely nothing to the game. They were just a fun little bonus that 360 users had. When Sony announced that they were pretty much going to copy them (but make minor changes), I groaned. Trophies actually may be better than Achievements. I don't know. Just the fact that they were somewhat of a ripoff has turned me off to the idea. I don't even try to get trophies. I scan the Achievement list every time I buy or plan to buy a game.