I shoot from .38 Special to .360 DW in my standard .357 Mag barrel. It doesn't seem to make much difference in accuracy, they will all shoot close to 1" at 100 yards. I also shoot from 125 gr (2200 fps) to 250 gr (1200 fps).
The 170 gr Keith bullet (Lyman 358429) will clock 1750 fps out of .38 Special brass using the "Keith .38/44 HD load" of 13.5 gr 2400 with a standard primer. Using Elmer's 15.5 gr of 2400 with the same bullet in .357 brass may shoot a little faster, but the .38s are fast enough for my purposes.
