Merrill,
The .32H&R is the old dog. The .327 is pretty much the newer version of the old 32-20.
That said, a few of us have been hot-roddin' the .32 H&R for a few years. Given good brass that won't round out the primer pocket...(anybody know how to spell Starline? ) and some proper loadings of the older .32-20 cast lead bullets......
It's ~ Hell on Wheels....