It's a little confusing. I'd say in general, quad-core processors are more powerful than dual core; however, that doesn't necessarily mean faster.
Certain programs are written to take advantage of multi-core processors, like many games and power-hungry programs such as Photoshop.
However, not all are. Windows does its best to distribute the load evenly, but it's not the same.
Furthermore, many quad core processors are clocked at a lower rate than dual core. Your dual-core processor is clocked at 3.23GHz; the quad is clocked at 2.66.
Bottom line: if the programs you will be running can make use of all the cores, you will very likely see a performance increase. If they are not designed that way, there is a good chance your performance will actually decrease.
In your case, I suspect the programs you will be running can make use of the 4 cores well; many games do. But use your judgment!