There's a $20 difference, but the 5770 supports dx11, while I believe the faster card is the 4890. Is the performance difference large enough to warrant getting the 4890? This is going into an i5 rig and is intended for gaming.
Current benchmarks show the 5770 being overpowered in sub-DX11 applications by the 4890, but as drivers mature for new ATI hardware, the performance generally increases steadily over time. I think the choice is purely about how important DX11 is to you.
Ignoring DX11 for a second, incase it isn't that important to you yet:
Also of significance, is that the 4890 will perform better comparatively as the resolutions go up. If you are gaming at 1650x1080 or under, the 4890 might be overkill, and the 5770 would most likely be lock in step with it. At 1920x1080 or higher the 4890 will pull away from the 5770. I don't think it is a deal breaking performance difference, as I would chose a 5770 over a 4890 if i was shopping for a new video card today. Even though I still only play DX9 titles (xp64) as DX11 is important to me.