Is playing an FPS at a lower resolution beneficial?

I have a 1280 x 1024 (4:3) resolution monitor. However, because my graphics card is absolutely horrible I have to play every game with the lowest possible settings.

Even then, games barely run at more than 10fps. To increase this, I always use a 800 x 600 fullscreen resolution. So the game is actually stretched to my screen.

Assume now a player with a certain amount of skill in a first person shooter who has 2 setups:

1. game running at 1280 x 1024 resolution with a 1280 x 1024 resolution monitor
2. game running at 800 x 600 resolution with a 1280 x 1024 resolution monitor

In what setup would the player achiev the best performance?

I was thinking setup 2 because the same amount of content is stretched to a bigger surface, however reasoning further makes my brain hurt...

Note: there are similar questions about stretching resolutions on Arqade but unlike those I'm not interested in the effects on the graphics card.

Edit: removed the framerates as they aren't really relevant.