A new I3 can beat an old quad! A quad is better for multitasking but if you are running a single threaded application then a faster dual can be quicker. Pretty much the only way to compare CPU's between generation is to look at benchmarks. Example http://www.anandtech.com/bench/Product/89?vs=289
For gaming most of the time the dual core will be better.
Most games don't use more than 2 cores, many games still only use 1 core for the core mechanics, other things like voice chat... might get offloaded to a 2nd core.
That means the 2nd core is not fully loaded and has ample room for background tasks (windows, antivir...).
For the same budget and thermal envelope a dual core will run faster.
If you run heavily threaded applications (video editing, photoshop...) or need to run many applications at the same time the quad core will be better.
The Core 2 Quad is also intel's first generation of quadcore processors, newer generations are far more efficient and can switch off unused cores. That way a modern quad core CPU can speed up its active cores if some cores are unused.