your quad core i5 2500k is more powerful for sure but for gaming, I guess your friends hd6850 would do better. His i3 2100 is still a pretty good dual core cpu and it certainly wouldn't bottleneck the hd6850. Hence his rig is better for gaming.
Tho you may get better frame rates in some games that mostly use cpu. (e.g starcraft)however, that wouldn't be the case for most games.
If I had to pick one, I will pick yours but with 4gb ram and I will also think about upgrading the graphics card in a few months.
From a gamer standpoint, I would also pick your friend's system, the reason being that the advantage that your CPU brings, though massive for multi-threaded processing, is miniscule when it comes to gaming on 6770 instead of 6850. But the advantage that your friend's GPU brings in is considerable even when coupled with the i3. Moreover the i3 on its own is not a bad CPU for everyday use.
In my opinon, a boost of 10 fps across the fragile 25-35fps range is way more worth than a 10 second shave off processing time. A deficit in the latter is tolerable but not the former.
i would pick your friend's computer.. 6850 is better than 6770. even though your CPU is much much better, it's not a MUST for gaming. i3 can handle 1080p res just fine. But for everyday overall work, yours is better. from a strict gaming point of view i would pick then one with the better GPU :-)
Note: his rig also has usb 3.0 and sata3 support. (edit : yours doesnt)