The drive will not boot on the Dell because all of the motherboard / chipset drivers would be wrong. If there were no Dells involved, I'd suggest trying the move and a Repair Installation from the Vista installation disc, but with a Dell in the mix I would never try it.
In addition, if Vista came with the laptop you would be violating the license.
Dell should be able to give you a recovery CD. You could put a new drive in the Dell, run the recovery CD, and get a factory-fresh system.
Do you need to recover data from the XP drive? Come to think of it, are you sure it is a drive error and not a problem with your version of the OS?