Q:

Would the Nazgul have been greater in power if they had their rings?

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? 

A:

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.

