The percussion revolvers are pretty fun, but I also find them messy and inaccurate. Pyrodex or a different synthetic powder would help with the mess.
I had a .44 (1861 Army)for years, until a friend blew it up by forgetting to grease the chambers. He pulled the trigger once, and five chambers fired. One down the barrel, three down the sides of the barrel, and one right into the back of the loading lever. I loved that gun, but having made the switch to single-shot pistols, I won't go back to a revolver. My accuracy improved radically when I was taught to point-shoot it and ignore the sights. I actually removed the front sight eventually.
Power-wise, both are inadequate for hunting anything other than small game. If you're poking holes in paper, it doesn't matter what the caliber is. Chances are you'll need to order balls through the mail, unless you have a black powder store near you. Most stores don't carry the .451 or .454 balls for the .44, or the balls for the .36 either. If you hunt with it, the .36 is great for squirrels, and won't destroy as much meat as the .44. Most squirrels will be pretty safe anyway, hehe!
Both will be fun for plinking, but like Saxman says, for historical accuracy, I'd pick the .36 over the .44 if you choose the 1851 replica, since the .44 isn't an 1851 replica...
If you're looking for more power, accuracy, and a higher rate of fire, you'd be better off to go with a single-shot pistol. I can load and fire a flintlock pistol 10 times in the time it takes to load and fire the revolver once, for six shots. I have much more power, and much better accuracy. I just sold my .45 flinter, and am in the process of building a .54 flinter for hunting deer. It's also nice because it uses the same powder, patches, and balls as my rifle (as well as all of the cleaning tools).
