I don't game much, but my experiences with the 2 card companies are the following:
TV-Out
My buddy couldn't get his MX440 card to display a proper TV-Out picture no matter what he tried. Different drivers, all the versions of TV-Tool he could lay his hands on, nothing helped. The TV-Out was jumpy, noisy, blurry and plain unviewable. My Radeon 9000 Pro on the other hand, has no issues at all at displaying on the same TV set. At first I shut down my computer to hook the TV up, but recently I noticed that I don't need to do that, just hook, click the button in the drivers' Display tab, and watch. Switching the primary (video capable) and secondary display is also a breeze. And it's pretty crisp and vivid too.
Windows Capabilities
On the same friend's PC with the MX440, when I try to drag a window of Media Player, playing a movie, the picture disappears and I drag a black rectangle instead. When I release the mouse button it takes it a good 2-3 seconds to show the movie picture again. Same thing happens when he shuffles the timeline. Not so on my Radeon. I drag movie windows, and you can see the movie still playing even as you drag it. And no blackouts when I release the button, or when I shuffle the timeline.
Game Compatibility
One thing the MX440 does better is run GTA3 and GTA4 (this one to a lesser degree, it's pretty much the same on the Radeon). GTA3 was choppy on my computer, even though I think the 9000 Pro is a more powerful card. All other games are about the same or slightly better.
Now I know his MX440 is a low-end card, but so is the Radeon 9000 Pro. And in my eyes the Radeon is a much better all-round card, meaning that if someone would ask me what card to buy I'll recommend ATi before NVidia.