I shoot a Banker's Special which is a snub version of your revolver. When using factory loads it prefers the .38 S&W that I've tried over the Remington .38 Short Colt. I hand load and, while I've not slugged the bore, a .358 diameter 158 grain semi-wadcutter over a moderate charge of Unique is quite accurate in this revolver.
The Police Positive family of revolvers are pretty robust and will easily handle any stresses produced by either the .38 Short Colt or .38 S&W rounds. Don't be concerned about favoring one over the other.