I run Garry's Mod natively with Radeon drivers on my HD5770 and it runs pretty well. Highest settings @ 1280x1024As for TF2, I'm not sure what sort of hardware acceleration it may require. The ATi driver doesn't have as much to offer as NVIDIA, but there is some available.
Also ran it through Wine with the highest settings
Performance isn't as high as it is under Windows but it's quite do-able.
Why not give the Radeon drivers a shot as well? Just make sure you get the ATI power profile extension if you're using Gnome.