I have been debating to sell my AppleTV for a 360 for a couple of months now and still haven't decided if I should keep the AppleTV. My roommates and I have the holy trinity (wii, ps3, 360) and an appletv, so I have been able to experience the best of all worlds even though I'm not completely sold on any one product for video watching purposes. I want my parents' home to be nice whenever I move back.
The advantage with the
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TV is that it is very classy, as someone has stated above. The interface is sexy in comparison to the 360 and PS3 because it's clean and simple. The remote is very elegant and simple click away. My library on the AppleTV's organization parallels my iTunes library, which plays a pretty big role in the classiness. Definitely a winner if you have a female companion over
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As for the 360, you definitely need Connect360 (like 20bux?). There are a lot of advantages with the 360 but a couple of drawbacks. A lot of my ripped TV shows are in DivX, so converting is a bitch on the AppleTV. With the 360, I don't have to bother converting and just leave it there. Being open to DivX and XviD, as well as mp4 and such, this thing is open to my entire library of music, videos, as well as photos (although AppleTV is so much nicer when it comes to photos). My biggest complaint is that the 360's organization is pretty fugly. When you choose to share/stream a lot of videos, say TV shows for example, from one main folder (like I do), you better name the file name appropriately, like TV Show-Episode Number-Episode Name, because it is alphabetically organized by file name. Not all my TV shows are labeled that way (a Folder separates the different shows). And using the 360 controller to select your video file/music is pretty unappealing. That said, 360's Visualizer is awesome.. Apple better put it in a later version(!). Obviously, if you don't have a DVD player, 360 fxns as one pretty well (although UI is ugly, again). And video games are a huge huge plus.
So to sum it up, I'd have to say if you're a person who's after the elegance of a media player, trying to impress someone (hell that could be you too!) and understands that you have to sacrifice time to achieve beauty, the AppleTV is the way to go.
If you're a person who thinks video games and a DVD player is a first and streaming all your content is an awesome add-on, then the 360 is the way to go.