'Are there advantages to using the horns? It would seem they provide a stronger attach point, though I've never had problems with just a rope".

No problem at all!!!! If your reefing lines are lead back to the cockpit, and are of 'small enough' diameter its a good idea to pass one or both of the lengths 'through' the open space of the gooseneck ... helps the reef line)s) from getting fouled on winches, cleats, etc. on the mast and helps to keep the reefed tack more or less on the centerline of the boom. ;-)