The primary reason for the BM base pin is to prevent the factory pin from "launching" when fired. Some guns have a weak lock spring or some other issue that causes the pin to fly loose.
Another side benefit is the BM pins are slightly oversized. This will tighten the cylinder movement a little.
Ruger designed the BH and SBH to be a little loose. When fired, the bullet forces the cylinder to align with the bore. Cylinder side play (horizontal) and the base pin play (vertical), provide the needed slack. If the cylinder-to-bore alignment is off a little and there isn't enough slack, the bullet will shave. This results in spitting from the gap and a loss of accuracy. Most guns either stay the same or improve accuracy slightly with a BM base pin. Some are off far enough where the tighter pin will actually make the gun less accurate.
If you gun is shooting well and not launching the base pin, then there really isn't any advantage to the BM pin other than it might feel a bit tighter.
