It really dpends on the card.. size of the VRAM and more importantly the BUS width. The 4890 holds its own very well at high resolutions compared to the current gen just as the 8800GTX/Ultra did before it.
(I have been eyeing up upgrading my 4890 and so far the only thing that can be called an upgrade costs way too much for my 1920x1200 gaming.)
I was talking specifically about Crysis, I know the hit isn't as big with other games. And my previous card was a 4890, its a great card, still performs great today. Only reason I upgraded is because I wanted something to last me longterm, and my brother wanted a good gpu for his computer, to meet his demands (Games running well at decent settings, no bleeding edge surround 3d monitor @ 128xAA for him)
My new 480 is great, don't get me wrong, but right now there really isn't much out that'll show a big difference. Crysis is a lot better, and Metro is MUCH better. Other than that, its been small things like turning up AA a bit more because theres not a lot out there that can push a 4890 hard, let alone a 480. So if you don't need it, you can probably hold off and wait for either a 5870/480 to drop way down in price, or wait for the next series of GPU's.