We have done both, but our Cozumel experience was prior to the hurricane so I can't say if it would be the same now. Neither of the barns Disney uses had any signs of horse abuse (and believe me, I would know it because I've been a horse owner for the past 25 years and current own two hooved "babies"). I did see some horses in bad condition at Xcaret, though, when we did a RCCL excursion there.
In Cozumel, we were allowed to trot and canter in a couple of spots, and after the ride, a man had his trick horse perform. It was a stallion that had been abused, but he retrained it using natural horsemanship. It was so calm that it laid down while people sat on its saddle for photos.
In Costa Maya, it was all walking the first time we rode. When we did the ride last week, they allowed those of us who wished to to trot or canter in a couple of spots. It was all very controlled and safe.
I would recommend either excursion, although as I mentioned, Cozumel might not be the same now.
Barb