^ I agree and disagree. I recently upgraded the 4850 in my HTPC to a 6850 and there was a big difference despite the 2.66ghz C2D in the system. It's admittedly the 4mb L2 chip but the 4850 is also significantly faster than his 3870 and not much slower than the 5770 (once you factor out the framebuffer difference).
But, really, the OP can't go wrong with either. The added cost of a 6850 will pay off in the future while a 5770 will also bring big gains today.
No doubt there should be an improvement, but all these little things add up to make your situation different:
1) Your extra cache certainly helps. C2D loves cache for gaming. So his system is a tad worse by a few percentage points.
2) The 5770 is probably faster than the 4850 than you think:
http://www.anandtech.com/bench/Product/177?vs=172 In the more GPU-intensive situations (Crysis, HAWX, Wolfenstein) it's about 30% faster.
3) You were probably gaming at 1080p for your HTPC, weren't you? If so then I'd say that is yet another situation that is more conducive to let the 6850 shine, at least moreso than 1680x1050.
He can get the 6850, it's a fine card, but I think he should only get it if he plans to migrate it over to a new system or if he gets a bigger monitor. That's my advice. Just to clarify I don't think he can go wrong by grabbing the 6850, as there are some games where it should make a difference, but I think the 5770 is just a better fit. Start saving up for a processor or system upgrade.