I'm at my office, away from my reference books, so you'll forgive me if I have to run off brain-fumes ...
But, as far as has been ever determined, Colt made the 1851 Navy in only two calibers: the standard .36 caliber and a few experimental revolvers of .34 caliber. Or was it .40? I can't remember which. Anyway, as far as regular production and procurement by civilians and the military, the Model 1851 was only available in .36 caliber.
Colt referred to this model as the "Belt Pistol." Because of the naval battle engraved on its cylinder, it came to be known as the "Navy." In truth, the Army purchased far more of the Model 1851 than the Navy did.
I'm really fuzzy-brained on the 1860 but I think it was initially called the "Holster" or "Horse" Pistol. Anyway, I know that bullet moulds intended for this model are marked with an H to indicate their use. I just can't recall what that H referred to.
As for the 1851 Navy in .44 caliber, I wouldn't suggest it. Because the cylinder is intended for the smaller .36 caliber, it doesn't have as much powder capacity as the other .44 calibers.
I had a Navy .44, brass-framed, back in the 1970s. As I recall, my maximum load was 30 grains of FFFG black powder. That's all I could get in, and still leave room for a ball (this was before I began using lubricated felt wads).
Heck, the .36 caliber Colt Navy will hold 24 to 27 grains of FFFG, depending on the maker.
My Pietta-made Remington .36 will take up to 30 grains, or slightly more if I don't use a greased felt wad. The Remington's capacity is a little more than the Colt's.
I enjoy my Remington .36, which sports a barrel of 6" or thereabouts. It's accurate but like all Remingtons, doesn't balance or point nearly as well as the Colts.
Experienced gun handlers --- whether the real pistoleros of yore, fast-draw enthusiasts or trick shooters --- have praised the Colt 1851 Navy as one of the finest balanced and natural-pointing revolvers ever made.
I saw a documentary some years ago, of a man twirling, tossing, back-rolling and holstering a Colt 1851 Navy. It was incredible how he could manipulate that revolver. I recall him saying that even the later Colt Single Action Army cartridge gun wasn't as well balanced as the 1851 Navy. When he wanted to put on a show, and didn't need to shoot, he used the Colt 1851 Navy.
If he was going to shoot, even blanks, he used the Colt Single Action Army cartridge gun since it was faster to reload (the audience gets bored if they have to wait whle you reload).
The Remington .36 is a good design, however. It's just not as balanced as the Colt. It's also more affected by powder fouling. The larger cylinder pin of the Colt, on which the Colt's cylinder rotates, shrugs off fouling longer. After three or four cylinderfuls, the Remington will drag and become harder to cock because of fouling.
But heck, it's a simple matter to pull the cylinder pin, wipe it clean with a rag, clean out the corresponding hole in the cylinder with a Q-tip moistened with soapy water and reassemble.
It's not like anyone's shooting back at you!
I'd suggest you handle both guns at your local gun store, if you can find them, and see which best fits your hand. Being comfortable with how a revolver feels is a huge step toward being accurate with it.
That's true of all pistols and revolvers, by the way, modern and antique. If it doesn't feel right in your hand, or feels clumsy, you very likely won't shoot it very well.
