From: Brussels, Belgium
AFAIK, every port can reduce sys dmg to 0, but only for ships that are disbanded in it (anchored, not in a TF). But it's not fast. As for the speed, it's not that simple.
There are two kind of repairs. The first is from the port itself, where size matters. A bigger port is better, and the number of ships in port doesn't matter.
The second is from repair yards, and there the number of damaged ships in the port matters. A repair yard has a certain value, and that's teh number of repair points "created" in a turn. For example, PH has a repair yard of 100, so it creates 100 repair points a day. To repair one point of damage on a ship, it consumes a number of repair points equal to its durability + 25. So, if you have several ships and their combined "cost" is higher than the value of the yard, they won't repair as fast as they could if they had no competition.
It also means that big ships like BBs or CVs should not be put in the same port as smaller ships (DDs, transports, CA/CL, etc), or else they'll never repair (at least not from the repair yard).
So, to answer your question, it depends. If there are not too many ships in the port, yes repairs will be faster in a port with a repair yard. Btu if there are too many ships, it won't do much difference, if the port size is the same.