I definately prefer the Western Caribbean. I have done each of the itineraries over 30 times!
The Eastern usually includes San Juan, Grand Cayman and St, Thomas.
The only one of the three ports that's worthwhile is San Juan. The Old City is beautiful and there's much to see and do on the island.
St. Thomas has gotten overcrowded and has been ruined by the vast number of cruise ships, daily. The duty-free shopping has gotten expensive because competition has been cut down. When you dump 24,000 shoppers into a town every day, prices rise. You're MUCH better off in St. Maarten. In fact, whenever I wind up in St. Thomas, I catch the ferry to St. John.
The Western itinerary gives you a taste of three very different cultures, Mexican, Jamaican and very British (Grand Cayman).
There are so many things to do in those ports!
Try rafting on the Martha Brae; wlking up Dunn's River Falls; visiting 9-Mile, Bob Marley's birthplace; etc; etc; in Jamaica.
Chankanaab Park, in Cozumel, is a wonderland; or visit a Mayan Ruin, in Mexico.
Take the Atlantis submarine in Grand Cayman....
By the way, Chankanaab Park is my favorite 'attraction' in the Caribbean.
Completely rebuilt and restored in1996, this beachfront park, just 9 km south of San Miguel, offers diverse attractions in a lovely setting. The main beach is studded with palapas for sunbathers, while just off shore there's outstanding diving and snorkeling (equipment rental and dive shop available). Back from shore is a fascinating Archaeological Park, complete with winding jungle trails, replicas from sites throughout Mexico, a typical Mayan village, and free guided tours. There's also an excellent Botanical Garden with over 300 plant species from 22 countries. Topping things off is the site's beautiful lagoon - a sinkhole filled from the sea by underground tunnels. There are several shops, snack bars, a restaurant, and a Mayan Museum. Open Daily. Admission is $12 US and children 3 to 11 years old $6 US.