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.
CPU comparison (i3 2100 vs i5 2500)http://www.anandtech.com/bench/Product/289?vs=288
GPU comparison (6850 vs 5770)http://www.anandtech.com/bench/Product/539?vs=538
6770 was not available for selection so selected 5770 instead for comparison as 6770 is in fact a rebadged 5770