They are both pretty much the same to me, especially given that most multiplatform (if not all of them these days) will have the exact same achievements or trophies in each.
I still prefer achievements because it is integrated better. A gamerscore shows the total achievement points you've racked up, but I haven't found a simple way to check on a friends thing (without going through the friendlist and checking their id tag) how many trophies they have, also I'm not sure how many I have in total (I know how many I have per game though). One nifty thing I might add about trophies though (which I don't think achievements have) is that you've got a percentage of the amount of trophies you still need to get per game, as opposed to achievements where I think it's the amount of points you can still obtain (rather than a stat showing the number left to obtain). I could be wrong though.
I probably care less about trophies because I started with achievements (and hence the novelty value has worn off).