After switching to a 6800 XT I found my VR frames were much worse than the 1080 I had before and there were constant stutters. Turns out the only way to get correct performance is to disconnect all other display devices while in VR. This means you have to start SteamVR, disconnect your monitor which tanks performance to 1 FPS, then restart SteamVR by changing the refresh rate to something else then back to make the 'restart SteamVR' button appear in the menu.

Don't fall for the AMD meme, in other words.