Well, to be honest it depends on the motherboard/RAM.
DDR3 is definitely faster, and anything over 4GB for most games isn't necessarily needed. It can also depend on the size of your pagefile/swap space. Generally speaking the pagefile/swap space should be 4x the size of your RAM.
As for the motherboard, if it's DDR3 compliant, is it tri-channel or dual channel? If It's Tri-Channel and you're using 2x2GB RAM cards, you'll actually lose performance. If it's Dual Channel, you'll be better off with 2x2GB DDR3.
As for 6GB of DDR2, you're most likely losing performance as DDR2 is only dual channel. Thus the only way you could achieve 6GB is 2x2x2GB or a 4GB and 2GB. Either way, you would be mixing RAM cards, losing sync and whatnot.
It also depends on the type of RAM. If you're using Kingston budget DDR3, you may see similar performance in relativity to overclocked performance DDR2 Corsair XMS2.
Inevitably, I'll require more information to give you a final verdict.
Also, a bit of history about DDR. DDR is an acronym for Double Data Rate, which means it provides two interfaces for each differential clock. DDR DIMM, or DDR1 (DDR) maxed out at 400Mhz, while DDR2 picked up at 400MHz. However, due to latency timings, a 400MHz DDR theoretically could outperform a 400MHz DDR2. Likewise, the highest performing DDR2 compared against the lowest performing DDR3 would result in better performance by the DDR2 due to latency timings.
The more you know, and knowing is half the battle.