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.