Well, Crysis is pretty demanding which could be due to inefficient coding. Crysis: Warhead runs a little better, but I haven't played it because of DRM (copy protection) only allows around 5 installs before it's necessary to call EA.
I think with your HD 4870 you will probably get mid 20's to high 20's on a 22" monitor. With a 1080p monitor you can probably get low 20's.
If you were to play Fallout 3 (the game I'm currently playing), then you can expect frame rates to top at about 70FPS @ 1680 x 1050 and about 60FPS @ 1920 x 1200 (close to 1080p) with everything set on high, based on benchmarks I've seen.