I compared graphics of Skyrim with my friend who has rather inferior computer in comparison with mine; not sure with details, only of his graphic card (GF 8800 gt 256 MB RAM), basic dual core Intel and 2GB RAM + XP SP2.
EAH4870 512 MB
8 GB RAM
Win 7 64 bit SP1
Technically speaking, your 4870 should be better, although the amount of VRAM with the 8800GT should be 512 RAM, not 256. But, for this game, the 4870 might not be nearly enough to play the game at 1600x1000 resolution, while the 8800GT would scale better at your friend's resolution of 1024x768, and on Windows XP as well.
You should use latest ATI drivers, and also pay a visit to Skyrim Nexus where you will find a mod (amongst others) which will enable you to use more than 2GB RAM, as the game is currently using out of the box. Also, let us know the details you're using while playing the game.
I have everything on max, except for AA settings (0 samples) and AF (8 samples), resolution 1920x1200. In advanced menu I also have everything on max (distances, etc.).
I even tried lower resolution and medium settings (as my friend has) with no improvement.
go into ccc an turn up the mipmap and texture map levels also go into the games settings and turn up if you still have no luck then head over to the skyrim nexus. you will find game optimizations and other apps that will help improve the overall quality of the game.