Okay, you already know the 1851 was never offered in 44 caliber.
And the frame size of the 1860 and 1851 is the same.
The cylinders are identical so they will hold the same charge of powder (as I recall only up to 30 or so grains).
So the question becomes "How do you like your barrels: round or octagonal?"
Me, I like them round, of the dozen revolvers I own, only two are octagonal, and they were gifts.
Another plus for the 1860 would be the rammer. Not only is the creeping style a bit more powerful but it is made for the 44 caliber where the one on the 1851 is proportioned for a .36 caliber projectile.