I have used both barrels for quite some time. The 'round bottom' or radius rifling in both is somewhat different so it's not an apples for apples comparison. The Rice barrels use either a true square bottom rifling, like the green mountain barrels, or a radius bottom, which is essentially a square groove with a slightly radiated bottom to the groove. In other words, in profile, cut a square in half an then add a bit of an arc to the bottom. Colerain, on the other hand is a really deep round groove, like a big "U" shape. If you look at the old photos of the muzzle of the Ed Marshall gun that George published in RCA 1, that's what you get with Colerain.
Both barrels will shoot very accurately, much more accurately than I can personally shoot.
I find the Colerain barrels to require a thicker patch to prevent burn-through as the grooves seem to be cut more deeply, but on the other hand, the Colerain barrels seem also to be more forgiving of various loads and patch thicknesses to obtain the same accuracy. At the end of the day, I don't think you can go wrong with either. Also I have dealt with both companies personally and found both to be VERY attentive to the satisfaction of the customer, so it's a draw there too. Scott Keller at Colerain whipped me out a completely custom smoothbore barrel in about 3 weeks once, and the Rice guys worked with me to stretch out one of their profiles to 46" length which became the 46" rifled barrel they sell, so ultimately, I think both companies are representative of the penultimate in customer service and super nice people.
I think ultimately it's all going to come down to exterior finish, which I must admit, gives Rice a marginally slight bit of an edge. I've not had any breeching problems with either company as well. I would be perfectly happy building a rifle with either barrel.