IIRC, as the cartridges were loaded by the Frankfort Arsenal for the Army, there really wasn't a great deal of difference, powerwise. Military specs for .45 Colt ammo called for a 250 gr. slug over 30 gr. of powder and a 230 gr. bullet over 27-28 gr. in the .45 S&W (Schofield). Due to the mentioned logistics concerns, Frankfort began producing only the .45 S&W cartridges for issue in February of 1876.
IMHO, as loaded by the military suppliers relative performance between the two was pretty much a "wash" for most practical purposes. Also just MO, but not only is it more "authentic" to shoot .45 S&W ammo in your repro Schofield, it should actually function a bit more reliably and hold up longer without needing to be "tightened-up" at the hinge and latch, too.