Obviously the Sony people didn't immediately realize the power and scope of XB360 achievements system, however they certainly did a great job with Trophies.
In the end I actually think that Trophies do a much better job than achievement for 2 main reasons:
1) Trophies deliver more (visual) satisfaction than achievements.
When you look at your trophies lists and all the bronze, silver, gold and platinum cups the satisfaction delivered by platinum-ing a game and by looking at all those neat cups is certainly visually but also intrinsically more appealing and satisfactory than looking at some more sterile points count.
Of course that's the same concept but visually and conceptually speaking the little trophy cups certainly do a better job that the icon+points system of the XB360-Obviously everyone will have their own opinion, preference and whatever but still no one can deny that the platinum cup is a quite fulfilling piece of graphic!
2) The second reason is perhaps more of a personal preference rather than something that can be considered an objective statement of facts and it's about the visual organization: trophies are more clear and cleanly listed and therefore it's easier to go through them, check etc., they're better arranged visually.
When you unlock an achievement this goes at the very top of your achievements list, to show the latest achievement you got.
On the other hand trophies always keeps their place in the trophies list, the list is always the same and it's therefore easier to check which trophies you got, you missed and so on since they are usually listed to match the game/story path/development.
This means that if you are missing some trophy at the beginning of your list you actually missed something at the beginning of the game and so on.
Easier to check, easier to see when you missed things etc..
And of course once you complete a game you have that lovely platinum cup on top of everything else.
The truth is every gamers will probably prefer the system s/he is most accustomed to.I got my PS3 much before my XB360 so I'm more used to it and, generally speaking, I like the PS3 crossbar much more (perhaps even because I was so accustomed to it through my psp) and always found the XB360 layout/graphic less stylish and a bit more childish although I really LOVE having my custom avatar!
So if you mostly use your XB360 you're more used and care more about achievements, PS3 users on the other hand will likely prefer trophies and so on, still I think the trophy implementation is really spot on although it took a while to have it ;).
Enjoy your gaming!
Ivy