If you are shooting in a NCOWS/CAS match where you don't have a table/shelf/bench:
Colts: Push out or remove the wedge, remove barrel, remove cylinder. You now have 3 (or maybe 4) pieces to hold while reloading the cylinder. (Frame, cylinder, barrel, and maybe wedge if it wasnt retained in the barrel)
Remington, lower loading lever, pull base pin, remove cylinder. You now only have 2 pieces to hold on to while reloading the cylinder (frame & Cylinder).
Of course, if you are just shooting for fun, off a bench, it really doesn't matter cause you can set the pieces on the bench and take your sweet time doing it.