Personally, I prefer achievements.
I like the instancy of them in that I have this running number and that's it. If I want to compare with a friend I simply look at one easy to find number. If I want to dig further down, then I just start comparing games. It's simple and quick and I like that. I also like that I don't have to do any syncing, it's all just automatic.
The only up that trophies have over achievements for me are platinums. I do like looking at someone's trophy card and seeing how many games they've 100%'d.
-edit-
Oh, and how could I forget the sound!
I love the little ding you get, it's so satisfying. Whenever I'm watching something on Netflix and someone signs on, I always pretend I just got an achievement and tie it to what just happened in the movie. :-p
