I would recommend Clearwater. The water on the gulf side is much calmer and easier for kids.
You must be very careful on the Atlantic side. There are always lots of riptides. There are often jellyfish. The surf is often very rough. I hear of shark bites on the Atlantic side every few weeks. I never hear of that on the gulf side. I'm not saying it couldn't happen there, but I just don't hear it.
In general, I hear of a lot more people getting in trouble on the Atlantic beaches than on the gulf beaches. It is not unusual for lifeguards on the Atlantic beaches to make multiple saves in one day.