The 500T uses ceramic magnets, which are generally brighter sounding and more powerful than the Alnico V magnet in your JB.
The 500T is a super-high output "in your face" pickup, whereas the JB is a hot-rodded PAF, more round and "classic" sounding. It will take some getting used to, and some more amp tweaking, though I don't know how close you'll get to Green Day with a solid-state Peavey. And I'd put the pole pieces back where they were, they're really more for balancing string-to-string volume.
Mike