I think the "Sharps" rifle is a very strong action, but traditionally used for relatively low pressures. The action will probably stand much more than has been "proof tested", but I wouldn't experiment. I'm absolute positive that the Pedersoli replicas will withstand any off-the-shelf factory ammo without any problems. It's only when you start handloading that you realize the full potential of the old "buffalo" cartridges, but most of the top-end loads are way too much for the old actions like the Trapdoors and lever-actions.
Falling block actions are some of the strongest actions ever built, but if you start monkeying around with unproven loads, you are risking embarrassment, the cost of your high-dollar rifle, and in the worst case, injury. I have launched some pretty hot loads from my Pedersoli 45-70 including jacketed 405 grainer's with Reloader 7 and IMR 3031 pushing 2000 fps.
I still prefer to shoot real black powder and big lead bullets because no matter how you shake it up, the 45-70 was designed that way.