I've stayed at the Caribe twice but never at the other Hyatt in Cancun so I can't offer a direct comparison.

My impression of the Caribe is that it is a fading older property, though still pleasant in some ways. Definitely in need of renovation (I don't know if this has been done since my last visit several years back).

The beach at the Caribe is gorgeous with crystal-clear water however the violent shore break made swimming hazardous. Definitely do not let your kids swim at that beach.

The two times I visited there was a real problem with aggressive timeshare touts harassing patrons walking between the lobby area and the elevator.

The Caribe is a five minute bus ride from the center of things in Cancun and a bus stops right in front of the hotel every few minutes.

Overall we enjoyed the Caribe but if we return to Cancun in the future we will stay elsewhere.