Honestly, with the exception of the fact that they both address American history, that is where the similarity ends.
Back in early eighties I had a friend that went to WDW and came back totally impressed. He wondered, however, how much it must cost to put the Hall of the Presidents show on so many times a day. It must have cost a fortune for all those actors and almost none of them had speaking parts. They just stood there and shifted back and forth or looked around. I had to break it to him that those were animatronics (robots) and not real people. The look of shock on his face was priceless. He had to ask a number of people if I was lying to him or not. It's a great show with massive detail. It makes me upset that people cannot get over their need for an adrenalin fix long enough to enjoy a real masterpiece in engineering and creativity. It is located in Magic Kingdom. (P.S. And it gets updated with every new President as they are elected)
After having said all that nice stuff about HoP, American Adventure blows it clear out of the water. If no words were ever spoken during the entire show, just watching the smoothness of the set changes and the complexity of the animatronics would be cause to manually have to close up ones mouth left open by the amazement of it all. Again, it's the current population of people that need others to stimulate their thoughts with high tension excitement that cannot appreciate the marvel that is American Adventure. The music is great, the show is incredible and the message is very clear. Not to mention the building is spectacular. It is the jewel of Epcot.
My opinion is that AA is the single most impressive attraction ever built. Exciting? Heart rate increasing? No. Thought provoking, emotional and close to perfection it is.