As a native Floridian, I feel strongly both ways.

I think it depends on whether you prefer the
ocean or a
beach with things to do nearby.
If you prefer the ocean, there is no question that anywhere on the East (Atlantic) Coast is better than anywhere on the West (Gulf of Mexico) Coast. There are real waves and lots of fun stuff to do
in the ocean. However -- on the East Coast, unless you are in South Beach (Miami Beach), Fort Lauderdale, Daytona, or St. Augustine, there really isn't much attraction
other than the water itself.
Many places on the Gulf Coast offer more in terms of things to do
away from the water. I haven't been everywhere, but I have yet to find the perfect venue. The beaches are all good, but there is a variance in lodging and things to do.
Lodging is very good at Marco. I think it's pretty good at St Pete Beach and Clearwater Beach. I love Longboat Key (Sarasota) for dining and shopping, but the lodging is pretty bad. Ft Myers Beach, Sanibel, and Captiva are okay IMHO, with the exception of South Seas on Captiva which is very good. Forget Everglades City.
The Panhandle is an unknown to me, because I have not been there, but many rave about far NW Florida.
I think the key would be to find a venue which offers the things your family
really wants to do on a Florida vacation.