The DX11 comment by Jack is irrelevant, since it has nothing to do with bandwidth, and it is something that the HD5770 can do, but the HD4870 can't do at all.
Looking towards the future do you think that either of these cards are going to be running at high resolution and high AA to choke a system? Or do you think it's going to be heavy shader and texture workloads that will start to slow these cards down in future titles?
Comparing the two, the shader capabilities of the HD5770 far outpace the HD4870, and even the HD4890 at times;http://techreport.com/articles.x/17747/5
But of course worry about the current titles, because since neither struggles there and one is a few frames faster than the other, why would you care about the future when games get more and more demanding?