For that hardware, which OS does not matter. They would all run equally bad. It will never be a 'gaming pc'.
I believe 7 uses less RAM to run so, yeah, Windows 7. But that's like saying, "Is a rock, or a stick better to defeat a tank?" The rock is, but it's not going to make a difference. You may scuff the paint a little with the rock
Windows 8 has 1 gig ram minimum requirements and it runs really well on my 8 year old centrino laptop ( 1gig of ram) so go for the 8.1