I would go with the apple TV, it does everything that the 360 can do with the exception of gaming and it cost less for both the unit itself and it says HD movies as low 3.99 which know for a fact the 360 there are no HD movies that are only $3.99. Plus even in the latest design of the xbox 360 model they are still known to have a 10% failure rate in the first year.
Actually, HD movie rentals on the 360 are 320 Microsoft points, which is $4. Also, how do you have the "first year" failure rate of a console that hasn't even been out for a year?
Back to the OP:
I'm a huge XBox fan, but if you're looking exclusively for streaming media the Apple TV is probably the better choice, or better yet, a custom HTPC. The Xbox does have a couple things the Apple TV doesn't: ESPN Streaming, and Zune Marketplace (which does have some free content). Of course, the iTunes Marketplace is much more robust and Apple TV does have MLB/NBA TV, so you do get some sports.
Basically, if you don't think you're going to want it for games, Apple TV is the better choice.
EDIT:
If your hoping to get streaming through your xbox360 especially 1080p using your laptop. The media center on my xbox 360 will only stream dvd quality from my laptop and even then it would freeze and drop signal here and there. Sorry but the xbox 360 does not have 1080p support. Maybe with streaming your personal videos if you can get it to work properly but MS does not provide any 1080p services through there software cause max 720p or 1080i. Not to mention very few xbox games are 1080p.
I agree with the others, if you just want to use the videos on your laptop get a netbook, way better.
A few things here. I just grabbed about a dozen 360 games at random to check, and all except for one of them supported 1080p. Also, the streaming problems you're talking about have more to do with the quality of the video than the actual video mode it's meant to be displayed at. Video encoded at a higher bit rate is going to have issues streaming wirelessly. I've encountered this myself, but found that there is no issue when working off of a wired network. Also, you can move your videos to some form of external storage and then hook them up to the 360.
I'm not saying it's perfect, but it's not half as flawed as you make it sound. PS3 has the same issue if you're trying to stream high quality video and both devices are connected wirelessly.