+1^ Rofl_my_waffle is right.
A HD5850 will give you a decent boost in FPS, and so the gaming experience will be smoother and more enjoyable, you'll also be able to apply AA (Anti-Aliasing) if you so wish.
Other than better performance there really isn't much difference, the HD5850 will obviously use more power and in turn produce more heat, but still at a perfectly acceptable level. Both cards have DX11 and other features like Eyefinity support.
I would suggest the HD5770 as its more than enough for the majority of games and will play Crysis fine with VH settings at 1440 x 900.