The Barney show is wonderful! My girls, ages 4 and 2, love it. There is a pre-show that lasts about 10 mins. (during which you have to stand, which gets a little tiresome) and then the doors open and you all circle a center stage in rows. If you get there early enough you will get to be in front, which my kids love. The show includes song and dance performances of all the favorites by Barney, BJ, Baby Bop and Professer Tinkerputt and there is a chance to meet the characters after the show, but it is like a circus trying to get in and the meeting is very brief, usually just a handshake, but fun for the kids. The show empties to a play area which includes a sand area, water table, building blocks, etc. Very nice and fun for the kids. You can exit through the play area or go through the store, full of Barney balloons, toys, merchandise, etc. To avoid a headache, we usually bypass the store, but they do have some great stuff - just pricey.
Just past the Barney attraction is the Woody Woodpecker Fun Zone which has a small roller coaster, a parklike play area and a wonderful water park. US also has the ET ride, Kongfrontation (a little scary, depending on how brave), Jaws, and Hanna Barberra cartoon ride which my girls love.
IOA has Seuss Landing which is entirely dedicated to kids and has 3 rides and one water park. My kids love it there and don't want to leave so my Hubby and I can visit Marvel Island for Hulk and Spiderman. My daughter (4) went on Spiderman, because she wanted to, but elected to bypass it on our most recent trip. Too scary for her. In Jurassic Park there is a hands-on exhibit that my kids love and there is a play area over by Bluto's water ride. In my opinion, US has more kids stuff but we still visit IOA each time we go too.