JRR Tolkien stated that Sauron kept the rings originally given to the Nazgul so he still had control of their wills.
"Who still through their nine rings (which he held) had primary control of their wills....."
From the letters of J.R.R TOLKIEN #246
So is it likely the Nazgul would have been even greater in power if Sauron didn't withhold their rings?
It's possible that they would have been.
In Letter 131 we read about the power of the Rings (with my emphasis):
But also they enhanced the natural powers of a possessor – thus approaching 'magic', a motive easily corruptible into evil, a lust for domination. And finally they had other powers, more directly derived from Sauron ('the Necromancer': so he is called as he casts a fleeting shadow and presage on the pages of The Hobbit): such as rendering invisible the material body, and making things of the invisible world visible.
Since it's established that the Nazgul no longer had possession of their Rings, it follows that they would no longer have been able to avail of this enhancement.
Of course that also means that if they had their Rings then Sauron would not have been able to control them, since he also no longer had the One (and he needed to hold their Rings in order to control them). In fact he must have taken their Rings back at some time during the Second Age (i.e before he lost the One) otherwise he would not have been able to control them following his return in the Third Age.
The end result would have been Nazgul with free will, although corrupted to evil and a lust for domination. No doubt they would have soon enough set themselves up as rivals to Sauron.
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.
