If we accept the idea that the rings are what kept the Nazgûl loyal to Sauron, it would follow that if they had their rings, they would no longer be subject to Sauron's will (or at least, not as subject to his will). While this might, at first glance, seem to suggest that they would be more powerful if they had their rings, it is important to remember that, were the Nazgûl able to exert their own wills, they would immediately become useless to Sauron.
Sauron isn't very tolerant of failure in his servants, and he would probably be even less accepting of disloyalty. If the Nazgûl got their rings back, they would have a choice: ignore their newfound free will and continue to follow Sauron's orders; or use their newfound free will to defy Sauron, and suffer his wrath. I can't imagine that the Nazgûl could just walk up to Sauron and say "We quit" without being killed before they had a chance to leave the room.
The books suggest that the flying fell beasts on which the Nazgûl rode were bred by Sauron himself, so it is entirely plausible that he could order the fell beasts to turn on their riders and kill them. We don't know whether Sauron was directly responsible for the Nazgûl's longevity, but it seems quite likely. This makes it possible for Sauron to essentially kill them all without lifting a finger: If Sauron is the reason the Nazgûl are immortal, he could presumably just say "Not anymore you're not", and all nine of them would drop dead on the spot.
As I see it, the Nazgûl might become more powerful if they had their rings, but Sauron would see to it that they also became more dead.