As others have said, I doubt the derailers themselves make a difference. The Specialized could just be slightly out of tune too. I have a 2003 Hardrock that shifts fine. When I bought it I thought shifting was decent, but a bit slow. After about 1500 miles I picked up a PC68 chain and put it on with 1 less link in the chain. I found that shifting was quickened up a fair amount and chain slap was also reduced.
The Deore derailer may or may not make a huge difference. It should last longer at least though. If the bike shop is willing to swap it out when you buy the bike they might be willing to take a few bucks off for your old derailer.