The former "we" used to have both. In his room there was a Roku and in mine AppleTV. It depends on whether you got a 4th generation or 3rd generation AppleTV. The 4th gens are supposed to be really cool. The 3rd gens are a lot cheaper. I have a 3rd gen myself. If you are really tied to iTunes, AppleTV is going to integrate really well. I think there are ways to set up a Roku to play your files and stuff with something called Plex, but I am guessing it is complicated. AppleTV fits like a glove if you are an iTunes maniac.
As far as services available... They do a lot of the same stuff, I'd say the Roku wins that one because Apple TV (at least the 3rd gen) does NOT do Amazon Prime streaming.
I guess Air Play is a possible workaround, but I never got it to work too well with anything I have tried.