I enjoy achievements, but tend to not go out of my way to get them unless it is a game I really enjoy or they are easy enough to get. Some games have achievements that require tens, if not hundreds of hours of grinding to do. That isn't fun. I don't really care if Nintendo adds them or not to their next system. What I do like to do is going back to see when I played games and seeing what I did in them. 

I enjoy collecting trophies.

I won't go out my way to 100% a game just for the platinum, but if I'm really enjoying a game I'll end up doing everything anyway, so having trophies to represent completion is an overall nice touch for a digital ecosystem, especially with photo/videos to commemorate your accomplishment.