Achievements vs. Trophies

“"I'm glad I did it, partly because it was worth it, but mostly because I shall never have to do it again” -Mark Twain.
These are the thoughts of most people after earning a really hard trophy/achievement. They're glad they've earned it, but mostly that they won't have to earn it again. But if both the trophy and the achievement have similar goals and the same feats, what sets them apart from each other?

Interface

After earning a trophy or an achievement, you'll be greeted by a graphic and sound clip. Everyone knows there is nothing more satisfying than hearing that glorious sound and seeing the name of that very annoying and hard achievement/trophy that you just earned. But the main difference I noticed between both is that a trophy takes a while longer to show up than the achievement, which isn't such a major problem but could give you some suspense moments at times.

Rewards

The rewards you get are pretty silly, but also really similar. While achievements earn you clothing or items for your avatar, trophies can also earn you clothing and items for your Home character/apartment.
Also, when you complete an achievement, you earn points that just keep increasing. You can earn the same amount of points by either finishing half the achievements of 2 games, or all the achievements of 1. Whereas Trophies have a different story. There is something called a Platinum trophy, which you earn by completing all other trophies, that gives you a major increase in your level(similar to Achievement's points, just by level) so earning half the trophies of 2 games won't earn you the same increase as earning all trophies of one game.

Conclusion

All in all there is no winner, it depends on your taste. The trophies come a little late but give you a bit more competition with the platinum trophy, whereas achievements appear instantly but points aren't as competitive.