Some clarification. The 1860 Richards-Mason conversion and the 1860 Type-II or Transition Richards are the same size (and they are both available in 45LC). The only difference between the two is the barrel assembly. They do both come with Army grips only. And of course the cylinder (and frame I think) are larger than the 1860 percussion gun.
The "1860 R-M" in .38 and the Type-II in .38 both have the same cylinder and frame as the 1851 R-M (non-rebated cylinder and non-stepped frame), with Army grips and 1860-style barrels. The .44's and .45's have the correct 1860 stepped frame and cylinder.
PJ, calling a '71 Opentop a conversion can cause confusion, since it looks a lot like a conversion but isn't as it was manufactured that way to shoot cartridges. With the two choices you mentioned to match up with your current navy-gripped OT, one choice would give you the same grip on two guns but different sights, the other choice giving you same sights but different grips.
To further confuse, although not with these particular guns mentioned, VTI lists the Man With No Name conversion (which is an octagon '51-style barrel on a '71 OT frame) as an "Uberti Richards-Navy"
And finally, I love my '51 R-M's! I put the brass front sight post on top of the hammer for a fast sight picture looking down that flat top of the barrel, and the rear sight on the hammer also makes for a much longer sight radius than with the OT.