Wife & I got married, honey mooned, and completed her OW certs at Sandals Antigua a month or so ago. We haven't been to Cayman yet, so I really can't speak to that but I thought I'd add my thoughts on Antigua.
We had a great time at Sandals (overall) but, it depends on what you want the honeymoon to be-a diving trip that doubles as a honeymoon or a honeymoon where you can also get some diving in. For a honeymoon site that also has diving (and for making your entire trip as stress free as possible) Sandals Grande Antigua was great. Now, there are a LOT of negative reviews of SGA on tripadvisor, so check them out fully before you book. We didn't have a single issue BUT there were a few people there at the same time we were that did. As far as the dive op itself goes, well, again...it's a dive op that's 'bolted onto' a resort, not the other way around. More cattle car type boat diving that some, more experienced, more individual divers would likely steer clear of, but overall the diving was pleasant. "Rental' (loaner, since it's included) equipment is SP (Pilot BCs & MK2 regs) that is in pretty good shape.
As far as the diving goes, yes, the diving on Antigua isn't generally as good as other locales in the Caribbean, but, if you haven't really done too much in other locations, the sites on Antigua are good for getting wet. As her first OW experience, wife had a fantastic time. But, again, she didn't have any other experiences to compare it too. Overall, mostly smaller reef fish, with some nurse sharks, reef sharks, a turtle here or there if you're lucky, and on her OW 3 a lone dolphin shot through the 'theater' about 20 yards or so in front of us as we were making our way back to the anchor line.
Anyway, hope this helps, and if you need any more info, feel free to hit me up on PM!
-Stacy