I use my xbox360 for media streaming every day, mainly TV Shows and Movies, and this is where I feel it falls down against the
tv.
I use a program called Twonky Media and is able to stream to xbox360, ps3, other computers and my iPhone through browsers.
Still, the problem with the xbox360 is the interface and the fact it doesn't use metadata for organizing video.
But still, if you can't afford an
tv, then using a current gen console would suffice for your needs. It will be annoying at times, but is worth it if you've already got an xbox 360.
If I had the money, I would buy an
tv, but at the moment the 360 will do.