Cayman will definitely be the better of the two dives - Jamaica was allowed to be fished out years ago - although it's gotten better lately from what I've read - no personal exp. there.
On Cayman the Carnival cruise operator is
Don Foster's. Every shop does a DM per 6-8 divers but some of the other operators are 6-8 max
per boat. I counted about 20 divers off a Foster's boat once - moored at the same site - our DM said "watch this"...
Other cruise operations in the area are several at Lobster Pot restaurant dock (it probably has another name),
Off the Wall,
Wall to Wall and
Deep Blue all have boats there. My pick would be Wall to Wall but I know the owner.
Divers Down is another option with a cruise program also. All are walkable from the pier - Lobster Pot is to the north.
Eden Rock was a shore dive 500' from the cruise dock (south) but a
container ship just scraped 150' or so of the reef clean and collapsed some of the caverns - IDK if they're even allowing divers there now due to safety concerns. The silversides on their webpage are only there in summer. Devils Grotto a few hundred yards south was untouched though afaik. IMO you could do better on a boat since they'll take you wall diving.
If you have the better part of a day, Turtle Reef is an option for
shorediving also - maybe
the best. If you do, dive south - there's a
tarpon cave in 40' a short swim down the mini-wall.
Probably a 30-45min. cab ride each way. Sundivers is on-site there and post dive there's the Macabuca Tiki bar for lunch. Their site is probably about the only with contact info for Ollen at Sundivers since they share the building -
http://www.crackedconch.com.ky/macabuca/ Allow for time for a cab to get there on your return also - it's mostly the only reason people go to that area - tourbuses go to other nearby attractions.
Just an fyi, Cayman is a tender port. And there can be up to
5-6 ships moored daily. I'd line up early although some of the tenders take over 200 or so. Cruise dive operations have it factored in - non-cruise dive boats leave between 8-9AM since they like to do 2 dives b4 lunch - some have a 1PM afternoon trip they need the boat for.