The 320 stream processors on a 3870 are not the same as the 112 on an 8800GT. A Geforce 8 series stream processor is quite a bit faster than what ATI calls a stream processor, but that is why they have so many more. I own both the HD3870 and an 8800GTX and while the HD3870 is a fast card, my 8800GTX is quite a bit faster especially with antialiasing enabled at higher resolutions. In general, the 8800GT is faster than the HD3870, although the card is no slouch, and does have Direct X10.1 support, if service pack one ever releases.
The only real benefit for the HD3870 that I have noticed compared to my 8800GTX OC2 is the color is much better with the HD3870. That’s it, oh and all games, the frames rates are hands down in favor of the 8800GTX. (all games that I own)
From what I read the 3870 has an insane amount of shaders but only a few texture units. The opposite is true for Nvidia's cards. The 3870 is mainly designed for dx10 as it is shader dependent(dx10 means a VISTA ONLY game...a dx9 game with "dx10" add-ins is still primarily using texture fill rate instead of shaders) and the Nvidia cards are designed more for dx9. Also in dx9 AA is done with texture units giving the reason for the 3870s poor handling of current games AA.
There are zero games that are true DX10 games (vista only seeing xp doesnt support dx10...new api and all) and therefore the 3870 and other current ATI cards wont perform up to what they can. Not sure why ATI didnt put a few more texture units in the 3870s so they could compete in dx9 but until a true dx10 game is released Nvidia will outperform ATI in games.
Don't forget AA resolve is handled by hardware in the HD series, whereas the GF8-9 series has dedicated hardware, which is fine for titles that do not require the shader based AA which both can do, but on which the HD series relies on for even normal AA.
Even though the HD series may have more potential shader power, alot of it depends on how it's used, and using the shaders is very inefficient if the app doesn't call for or require it.
OP, try a SEARCH next time, already asked already answered many times.