I have both Colt "open top" replicas and the Remington with the top strap. I've found that I much prefer the Colt design overall. Practical accuracy, ease of loading, etc. are pretty much equal between the two designs. Theoretically the Remington is stronger, but in the real world, the Colt is plenty strong enough, so no advantage either way. And it's already been noted several times that the Colt handles the inevitable accumulation of fouling better.
The telling feature that makes me prefer the Colt is that, when it comes time to clean, the Colt design is so much easier. The fact that you can easily remove the barrel and cylinder - the parts that get the most fouling - and immerse them in water for cleaning is what makes this so.
With the Remington you have to remove the wooden grip panels and detail-strip the action parts in order to give them a real cleaning.
And the Colts - especially the 1860 - just feel so much better in the hand.