[Updated/Solved - Open Source Driver is awesome! :)] AMD is useless for gaming
Dota 2: 10-20 fps + severe input lag (settings do not matter)
TF2: 20-30 fps + severe input lag (settings do not matter)
Unigine Heaven: up to 40 fps in Basic mode
Xonotic: 70 - 120 fps on low settings
Ubuntu Gnome 13.10
Phenom II x4 B55 @3.1Ghz
AMD 7770 1Gb + drivers from repo and AMD website (tested both)
This is ♥♥♥♥♥♥♥♥.
P.S. Vsync is off.
BIG ♥♥♥ EDIT:
It seems that after all latest RadeonSI (open source driver) and kernel 3.13 are the ♥♥♥♥!
After all my initial problem with those two was DPM, which I thought I set up correctly, but hey, I'm just a human :)
What u need for 60fps (when Windows gives me 80 in same scenario) in Dota 2 at max settings with card like 7770:
1. Kernel 3.13 and up, found in Ubuntu 14.04 for example (for other distros check google)
2. Latest version of RadeonSI driver, found here: https://launchpad.net/~xorg-edgers/+archive/ppa
3. Chenge DPM to performance, there is nice GUI tool for that:https://github.com/marazmista/radeon-profile
Have fun :)