They are both undead blood drinkers but I think the Rempires monster-in-a-Human-skin thing makes them a bit more interesting. Blampires are far too...zombie-ish.
Well the Black Court are supposed to be the traditional kind, sun light, stakes, etc. but a bit more disgusting. Red Court seem to be more the seductive, beautiful types that are about more now, but with a monster underneath. While White Court are Incubus and succubus.
JD if you've read Summer Knight you should be introduced to all 3 of those by now. All three kinds were at Bianca's party in Grave Peril.