THe reason the Convertible Blackhawk in 9mm is less accurate than the 38/357 is the bore size, as said. A 9mm is 354, and 38 is .357. 45ACP and the currently loaded 45Colt both use the same bullet diameter, so there will be no intrinsic accuracy problems.
The reason a Browning Hi-power strips lead bullets is not the bore diameter as Unspellable stated, as all the European 9mm pistols have true 9mm bores, not oversized. It is the very shallow and fast twist rifling, which is designed for Military jacketed bullets, that causes the tumbling. A Browning or other Auto equipped with a Bar-Sto barrel will not strip, as the rifling is deeper and a slower twist.
I noted years ago that the S&W model 25 or M1917 revolver would strip 45ACP lead bullets for the same reason, very shallow rifling, as the bore was designed for Military FMJ bullets.