We went to both parks when our daughter was the exact same age so I have a few cents... My daughter actually took her first steps while I was on Dueling dragons so it was quite magical for us! My hubby was proud to have a first happen with him!
Our daughter liked the talking fountain at IOA, it isn't a ride, but a fountain that appears to talk and interact, she could have stayed there for ages. She also was fascinated by the Cat in the Hat ride, ask them to turn the spin off. There wasn't a height requirement, but they did require your child walk. If the car spins it is possible to fall out so insist on turning off the spin. 1 fish 2 fish was also a hit although the wait can be long. Listen to the instructions so you don't get wet. (like a bumbo ride, but with water) I found the characters at IOA to interact much more probably because it was less busy than Disney parks so they might like this. Mine loved Sam I Am and the Grinch. Also, wander about the Suess area where they have bouncing water, pulling buttons, area, etc. Cute carosuel with Suess characters at IOA. The ship that is over by Pluto's barges is worth a bit of time if they walk, if not, pass on it. It has some slides, ropes, etc.
As for US we went but I don't do Barney so I missed that. She loved the Fieval area, but wasn't able to do much at her age. Lots of water play area so bring a change of clothes. Lots of cool things to look at. Plastic balls shooting everywhere.
I would be heart broken to go to either park and not do any of the adult rides. You can do baby swap and it's much better than Disney. My hubby and I took turns at US to ride Men In Black (singles line) while she was taking a nap and in IOA we rode Spiderman and all the roller coasters. They don't let your child even wait in line with you so be prepared.
I can't say which park to go to. If you got a hopper type ticket you could see the highlights of each park since there are so many and the ambience is part of the uniqueness.
Jenn