As far as performance improvement goes, two cores are FAR better than one. You should see an improvement in the area of about 5x better than the P4. To give you a better idea of how the performance would increase, here's an example. An upgrade like this would be like if I jumped from my Core2 Duo E6750 to a core i7 920. In 3dMark Vantage, my processor would get about 4500 marks. The core i7 920 gets about 16,500 marks. That's nearly 4 times better in terms of performance on that one task. It would be somewhat similar from the P4 to a Core2 model.
Now, I don't want to get your hopes up on this without being totally certain. You listed the model of the computer, right? A Dell XPS Gen5? I did a google search and it spat out some system specs on that model. As long as your computer is an XPS Gen5, then it's likely you have the 955X chipset. You can research this yourself and verify it to be safe. I don't want to tell you that your exact computer will support <insert part here> if it's not the same computer that I just tried looking up. That'd be false information and you'd be spending money on useless hardware. So double-check for me what model your system is and see if I'm correct.
You can also check the Device Manager for the chipset model. If you go to the Control Panel, go to System, Advanced Tab, and hit up the Device Manager, it should list a bunch of parts. Towards the bottom is one called System Devices. Open up that tab, and it will list a whole array of stuff. A little ways down the list should be something that looks like this:
Intel(R) G33/G31/P35/P31 Express chipset PCI Express Root Port - 29C1
That's the list of chipset models for my motherboard. My specific one is the P35. You should see something similar, just with 955X or 955 somewhere in the name. I know it's a little bit convoluted, but it's another way to be absolutely sure.