I stayed in the Mandarin Oriental and the Rosewood Mayakoba back-to-back, and found the Rosewood far superior on every count: service, rooms, food, pools, etc. The only way I'd encourage you to opt for the Mandarin Oriental is if you plan to spend all your time on the (very small) beach, since it's the same waterfront as Rosewood and is exactly the same. Otherwise, here are some contrasts:

Rosewood pools: spectacular main pool, with the best pool service I've ever experienced: at least every hour, and sometime ever after, they'd bring complimentary smoothies, frozen chocolates, cucumbers, sprays, etc., etc. The pool itself is multi-tiered, with steps rising up out of the water dramatically (a clever architectural play on the Mayan pyramid architecture endemic to the area). And the beachfront pool is nice as well.

Mandarin Oriental pool: small, cold, uninspired, with no service perqs to speak of other than plastic cups of ice water you can fill for yourself at the bar.

Rosewood rooms: you're taken by boat to your private dock, regardless of which room category you are in, you will have your own private dock and plunge pool. Vast bathroom, with the largest, circular bathtub I have ever seen (a clever architectural play on the local cenote pools, with a skylight directly above the tub). Rooftop terrace, plus outdoor shower, plus plunge pool. Superb.

Mandarin rooms: Nice, but not amazing. Outdoor bathtub, but can only be filled by calling to request bathtub service, and then the water sits and stagnates for days (we called multiple times to have it emptied, to no avail).