Yes, resolution does affect how a card performs. You can run at lowest resolution and have all settings on high, or run at highest resolution with lowest settings.
I'd say a 7800GT should be able to take most games at 1280x1024 at max settings. My 6800GT AGP with 2GB of ram can take BF2 at 1280x1024 at max settings except for 2-3 medium settings and NO AA, so I'd say the 7800GT can go fully max with 4xAA.
The 6800GS should be good for 1024x768 with mainly max settings without AA, but the 6800GT should be bale to perform 1024x768 at max with AA.
So to summarize:
1280x1024 Max Settings 4xAA: 7800GT
1280x1024 Semi-max settings No AA: 6800GTw/2GB of ram
1280x1024 Medium settings No AA: 6800GTw/1GB of ram
1024x768: Max settings 4xAA: 6800GT
1024x768 Semi-max settings No AA/2xAA: 6800GS