For its original purpose the Colt C&B, the Colt navy sized frame (1851, 1860, 1861) wins hands down. Its a faster gun fighting tool than even the SAA Colt. The lack of a top strap makes them point far better.
I never owned a Remington. Too clumsy, just did not "fit". Most problems with any C&B revolver are based on using a cheap revolver or using the wrong sized cap. I don't see this as being a big issue though if we look at the sales figures for the various Colt open tops and their copies like the Manhatten then compare the production of everything else. Its no contest.
272000 1851s
200000+ 1860s
325000 31 cal Pockets
40000 +- 36 cal Pockets
18000+ Dragoons.
Over 800000 revolvers from about 1848 to 1873.
Manhatten made 50000+- Colt copies though its tough to know exact numbers.
Remington, as best I can see, made 230000 of all models.
There are others similar to the Remington, like the Rogers and Spencer. But these were lower production than the Manhatten, but I have no figures. If the open top design was a problem with the C&B revolvers Colt would have changed it by 1860 since they had a LOT of experience by then.