If you are into all inclusive then yes, Caribbean might be better option. If you want to stay near beach and have options and variety, FL is better (or other southern beach towns). You can do Panhandles and look into JOE land, as well as visit New Orleans? You can do Fort Lauderdale/Miami and add days in Keys, you can do Tampa/Clearwater area too. I guess I like some variety and optionality when I travel.
California is wonderful in same way. I suggest San Diego/LA mix for warmer beach environment.
If I'm at a resort, I feel it gets monotonous after a few days and want local or ethnic flavors. But then again, can definitely find resorts that have a good kids club and even ones that cover dinner time for the boys, so you can enjoy some grown up meals.