Here's how I see it and explain it to people. (Now, these are generalities)
Eastern Caribbean: Hilly/mountainy Islands, lush, tropical. Beautiful secluded beaches in coves with bright blue water. Snorkeling is great in some areas, but not quite as good as some areas in Western. Eastern is a little more relaxed in general. With the extra sea day, instead of the extra port, if you want to sit and watch the world go by with a book in your hands, Eastern is for you. St. Thomas is a great shopping island and St. John is a tranquil location. Eastern draws more of a relaxation crowd.
Western Caribbean: Flat sandy islands with plam lined beaches that can go on for miles and miles. Great area for water sports. Snorkeling and scuba are second to none here. Many adventureous activities like 4 wheeling, jeep excursions, and a plethora of watersports. The western Caribbean/Mexico are know for activity. With an extra port day and ports that are know for their "partying" as well as their water sports (Cozumel/Key West) western usually draws the more adventerous crowd.
Now, of course, there is shopping on both and beaches on both, etc. etc., but I am just talking in general and after a number of cruises on a number of lines to both areas, these are my observations.