OK so I tested and, albeit odd, here they are:
For one monitor:
Settings:
Everything highest it can go, with 4 AA and DX11 (I would've gone for 8 AA, but all I have heard is that it just sucks frame rates for little better looks).
Average FPS: 57
Minimum FPS: 47
For two monitors:
Settings:
Most things high, some medium (I think), and post processing medium, with 4 AA and DX11.
Average FPS: 65
Minimum FPS: 42
I am not completely sure why two monitors have more FPS than one does. Setting up two monitors was a bit of a hassle (I have done it before this for the Dirt 2 demo), so I think something could have gone wrong in the resolution options on the game. So I don't think that was completely right. The pixels also looked a bit stretched, nothing like I have seen of Dirt 2 Eyefinity videos on youtube where they are not stretched at all.
So, as you can see the one monitor is better for gaming. It is a smoother ride with one monitor because of less flux with the FPS.
I think the 5770 should be better than decent for 1080p gaming as long as you have a bit lower eye candy. If you are the type of person that wants everything in his games to look the best but don't really care for that high of frame rates and can live with a lower FPS (probably won't go lower than 30 depending on the game), then the 5770 will do great. If want amazing frame rates though, you will just have to be willing to lower the AA to 2 or 0 and AF to 4 or 8, then the 5770 will also do great at 1080p.
I have heard that everybody says gaming is best at 1080p (or higher resolution), so if you want to the best resolution in gameplay go for a 1080p monitor, if you want all settings maxed out but with a lower resolution go for a monitor with less pixels, your choice. If you pick lower resolution I can help you decide on a monitor.