I've been on both, both are excellent cruises. I would say that the Eastern might be better for young kids. The Western tends to focus more on nightclubbing and party spots. At least that was my impression of both of them.
Both cruises have about equal access to beaches and such for the kids to play at.
Things that are highlights:
Western:
Key West -
Mallory Square. This is one wild party, all kinds of entertainment. Don't think it was that much of a kid friendly thing.
The Butterfly Farm. This is fun for kids, but they'll get bored quickly.
The main strip(I forget the street name) - Lots of Shops and Bars. Great for the party crowd, but don't think kids'll get much from it.
Grand Cayman -
Stingray City. An incredible experience, but I think small kids would be very intimidated by the open water and the rays.
Cozumel -
Carlos N Charlies. A huge wild bar.
Also there are excursions to Ruins, would be very boring for kids.
Sally's Mini Golf. This'd be fun, but it's not going to cover the day in port.
Chankanaab Marine Park. I havn't been there, but understand this is a family fun park, might be the redeeming thing for kids on this cruise.
Eastern:
St. Thomas-
Coral World. This is the highlight of the eastern cruise for the kids. It's a lot like Sea World, but in the Virgin Islands. Lots for the kids to see/do.
Paradise Point Tramway. This is an enclosed tram ride to the top of the mountain overlooking the port. They have a tropical bird show and you can get your family pictured with the birds posing on you!
St. John. Lots of beaches and such, it's one big park.
St. Maarten-
I don't have recent experience here, my understanding is they've added some family excursions, I think including a butterfly farm and some kind of dolphin thing, but I could be wrong on that. We did the semi-submersible tour and the reef was cool, the boats have huge viewing areas to see the sea life.