I just went from a p4 3.0ghz HT to an E6300 (1.86ghz), both in a desktop, and the Core 2 is faster. didn't overclock or anything.
The T7200 has a higher clockspeed and double the cache of the E6300, which should offset its lower FSB. In some tasks, the T7200 would be faster, in others, the E6300 may nudge it.
But, as said, without a doubt, the T7200 will be faster. With a clean Windows install on the notebook and a 7200 RPM hard drive, it should easily be faster than your desktop in nearly every application. I don't know what kind of graphics you have in your current desktop, but chances are the notebook you get will have slightly weaker graphics. That being said, if it's a laptop with any sort of dedicated graphics, it will handle just about anything you'd want
to do on a non-gaming notebook with absolute ease (including light gaming).