We have done both and I think most of the people who have replied have NOT taken into consideration your culture and food requirements.
Eastern only gives you 2 ports. Typically 2 of the following: Puerto Rico, St Thomas, Tortola, St. Maarten. Puerto Rico is a beautiful island with lots of great food and a diverse landscape. St. Thomas is America lite. St. Maarten/Sint Martin is a dutch/French island with a culture that reflects that. Tortola is the only one I haven't been to, but only because our ship was diverted.
Western gives you 3 ports, Cozumel, Grand Cayman, Falmouth. If you have the desire to ferry to the mainland and the ability to spend time on a bus, you can of course see world heritage sites in Mexico. Grand Cayman is largely a beach Island with aquatic wonders abound. Jamaica is a land that has some challenges with regards to safety but has its own culture and cuisine.
I can't make any recommendations on the food part of the trips as that is not an area I would be qualified to make a decision on.