From my understanding the Core 2 duo should work just fine with your system, as no other major system component has changed.
Here is a site with a direct comparison between the two processors:
http://www.anandtech.com/cpuchipsets/sh ... spx?i=2808
Basically, the Core 2 Duo is nice for a couple of reasons:
1) 64bit support (assuming OS is 64bit)
2) faster in CPU bound applications.
As the two chips you mention are both 2.0Ghz, you are unlikely to see much of a difference in games, because most games are not CPU bound, but the bottleneck is the graphics cards.