Well, I haven't ventured over to Ft. Myers Beach in a few years, once you fly in and go out onto Sanibel don't have a lot of reason to leave the island to be honest........I have a 11,10, and 6 year old and they love to go shelling and hang out at the beach skim boarding etc...........Ft. Myers Beach is more the classic Florida beach town, a little run down in spots, some beautiful new development and much more mini golf, movie theatres, every fast food chain etc............
Sanibel/Captiva is much quieter (although it can get busy certain times of the year and quaint roadways are not built to handle it)........more expensive and much more natural............basically at 10 pm they roll up the sidewalks and everyone is in bed, if your kids are looking to be entertained versus entertaining themselves the island will not be for them ( and is I believe a $8 charge every time you go on and off the island)...........but the restaurants are wonderful, the beach is fantastic and the scenery is beautiful............
Again if you choose to stay in Ft. Myer's definitely spend a day or two out on Sanibel and definitely go to the Mucky Duck (dinner/sunset) and the lazy Flamingo (lunch/late dinner)...............spend a day at Bowman's Beach on Sanibel (get there early), you won't regret it........................