handling characteristics- By all accounts, the heavy favorite is and probably will always be the Colt models. Does that mean the 1858 Remington's were impossible to handle? No, it just takes practice.
Winner: 1851 Navy Colt by a hair.
accuracy- Again, this comes down to practice and training. Having said that, a heavier bullet will be less affected by wind, but less of a flat trajectory and a longer barrel a longer sight radius.
Winner: Colt Walker on paper, but really inconclusive.
reliability- This is the era of cap and ball, the only reliable gun was a single shot. For revolvers though, most Civil War vets going home were buying up the Remington for a reason: they were easier to maintain and were allegedly more reliable. Also, they had the safety notches to safely carry the full 6 rounds.
Winner: Remington
loading- Gotta go with Remington here. Being able to take the cylinder out so easily meant loading off the gun was possible when not in combat. Even in combat, the potential for a cylinder swap was there, unlike the Colt's.
Winner: Remington
power- The more powder, the more power. Colt Dragoons easily held 50 grains of powder.
Winner: Colt Dragoon
durability- All the C&B guns could last a long while if properly taken care of. The way the Colt's came apart meant it was easy to clean the cylinder, barrel, and frame separately and gave easier access to the bore.
Winner- Colts
strength- More steel means a stronger gun, which would mean the Dragoon, but brawn doesn't always beat brains. The Remington design was a sold frame, the Dragoon wasn't, but the Dragoon could hold up to heavy recoil.
Winner- Tie between Remington and Dragoon.
I'd say it's a tie between the Remington and the Dragoon. The issue with the Dragoon was it weighed twice as much as the Remington did. Why would you carry one Dragoon when you could carry two Remingtons and double your firepower? You wouldn't, people back then didn't, and thus I give the overall edge to the Remington.