With proper ring design/material selection there will not be a big difference in engine performance unless it is a very high speed engine (10000 RPM) and higher. There are many ring designs and ring materials, as piston speeds go up with the higher performance engines, ring type selection gets more critical, for example many high speed engines use quite narrow piston rings to prevent ring flutter, the practiced ear can hear sometimes ring flutter, it can produce a distinct exhaust note warble, when this happens power definitely falls off.
Some high speed engines run fairly close piston skirt to cylinder wall dimensions so piston rocking with a single ring is greatly reduced in those cases.

For other engines, keeping the cylinder round under increased cylinder temperature (because of all the ports) could show a greater gain in power than the selection of a one ring design over a two ring design.