Even if the 5870 is bottlenecked, it would still perform a lot faster than the 8800GTX.
5870 is the way to go.
Yes, that's true, especially at 1080p res, cause then the GPU will do a lot more work than the CPU. But, to get most out of the 5870, OP should try and OC, 2.7,2.8 GHz should remove the little bottleneck. 3GHz and above if he's running low res ( like 1440x900 ).
8800GTX~HD 4770, so a 5870 which is around 2.3x-2.4x faster than a 4770, should be pretty much of a good GPU upgrade.