In comparison to the Xbox 360-
The ATV tries to provide a more fluid experience. I've never had the ATV pause to switch quality levels from SD to HD.
The 360 would pause for a second to switch from SD to HD or from HD to SD. We use a 6 mbps dsl connection at home and most of the time, the 360 would be in HD, but if anyone else used the connection, it would start switching back and forth between quality levels frequently, which was distracting.
The 360 has a quality level indicator, showing 1-4 bars and an HD icon when in HD. The ATV has no indication of quality.
The 360 displayed which movies or tv episodes were already watched and had a progress bar to show what percentage of the show was watched. The ATV has no way to indicate if you've watched a show or movie. This can be frustrating if you're watching a tv series with many episodes and you forget which episode you watched last.
The ATV has a much better looking interface. When you have a movie selected, you can get much more info about it (Actors and Directors) than the 360. You can then also click on the actors name and see what else is available by that actor.
With the 360, you can use your Kinect to talk to Netflix if you want (play, pause, fast forward, rewind). I feel stupid talking to my TV, so I gave up on this.
To watch Netflix on the 360, you must have a Gold Live account in addition to a Netflix account. This runs about $60 if purchased annually. If all you're doing with your Gold account is watching Netflix, it adds unnecessary cost. This is why we ditched the 360 for Netflix and got an ATV. Almost pays for itself.
In general, I like the ATV experience better, but it does have some flaws. It appears that Apple went over the top to keep the interface clean, which is nice, until you want to know which shows you've already played or want to know the video quality you're watching.
EDIT TO ADD- Also have a Vizio TV with Netflix built in. All though the interface has been updated since we bought the TV, it's still clunky and slow. But in the end, it does play the videos.