The HUGE advantage is that generally, once you've got it set up, it works. Things don't mysteriously change and stop working every couple of weeks. You can leave it switched on without rebooting frequently (this is only really useful for servers I guess). You don't really have to worry about the weekly updates although they are available.
At work I've got my old desktop machine running Ubuntu, along with all sorts of stuff I need for work, like file / web servers, databases. That was powered down for one hour two months ago due to the annual electrical testing, but otherwise has been running non-stop since last October! Can't say the same for my main Windows desktop.
I agree with Soleron on most of his points. Ubuntu is easiest to set up and use. You can't really use it on a games machine (but since you've got a console hopefully not an issue). Some hardware is tricky as the Linux drivers aren't as widely available.
I'd say don't try and put it on a new machine. If you've got an older machine, you can throw Linux on it and it's much more likely to just auto-install everything correctly. And the bonus is Linux runs much quicker than Windows, so it'll seem like a new machine anyway :)
Wireless networking is a bit of a mess (but I think the same on Windows - I've gone to Powerline networking instead now).