6100 graphics is integrated. it doesnt have any memory on it, it uses system memory.
ive never played BF2, but im sure that 6200 graphics doesnt play HL2 very well on high settings.
http://www.tomshardware.com/2005/02/08/nvidia_geforce_6200_turbocache/page10.html
in fact, there you go.
i can't find any benchmarks on a 6100 lol... that means dont get it.
im sorry i couldnt answer your question in amazing detail... but the answer is that both cards aren't really that great. i mean, i consider a 6600gt to be pretty bad/old.
oh! found a benchmark.
http://www.pcstats.com/ArtVNL.cfm?articleid=1966&page=8
it says that the 6100 graphics scored in the 700's in 3dmark05 lol.
compare that to the 6200 graphics... and its less than half as good.
the 6200 scored in the 1500's according to tomshardware... and in the 1000's for the 6200 with turbocache