Are we talking about pitch? or gauge? Big difference! The gauge makes very little difference, it is the thickness of the drive links. As long as there is enough material to support the cutters, and hold together under the power loading, and sufficient bearing surface for longevity, it will not much matter. i.e.: .058 will cut no better, or worse than .063. The only time gauge may make a difference in the cut, would be with a narrow kerf chain. It would be hard to make a narrow kerf on a thick driver.
If we are talking about chain pitch, then it is another story. The cutter length, width, and height, (as well as profile), have a lot to do with how fast a chain will cut, the power requirements, kickback qualities, etc. You don't run .404 chisel on your 36 cc climbing saw, or 1/4inch on the old 272 Husky with a 24inch bar.
Match your chain to the saw and the type cutting as best you can. You will have a safer and more efficient machine.