If your children are younger, Islands of Adventure is probably your best bet. First off, it has Seuss Landing based on the works of Dr. Seuss. A very popular destination that is a childs dream come true (whether they are fans or not).
There is also Marvel Super Hero Island which will have many of the characters your children love there for them to meet (Wolverine, Spiderman, Captain America, etc).
There is Toon Lagoon which is based off the many Sunday paper comic characters (Popeye, Beetle Bailey, Hagar, etc). There is a terrfic play zone and a few great water rides (provided they are 42+ inches tall).
Also, they have Jurassic Park. If your kids are into dinosaurs, this is a great place to go. They can see "real" dinosaurs (even you'll be fooled), and play in their park or discovery center.
Finally, they have an island based on myths and magic. The rollercoaster there may be to much for them, but they have a smaller unicorn coaster for kids. Stay away from Posiden (long dark show that may scare little ones), but totally bring them to the Sinbad show (a live action show with magic and tricks that they will love).
Studios has Nickelodeon's Jimmy Neutron and Shrek, as well as ET, but little past that for kids. Jaws may be to intense, as will the mummy. Earthquake and twister are kinda intense also. They have some great shows, but for families with children primarily under 10 years old, I'd sugget going to Islands of Adventure. Save the Studios until they are a little older.