Hi Andrew, another St. Louisian here.
The DL version is much more intimate with your seating practically on top of the action. It draws you into the story more.
However, I can understand Disney's reasoning on building the amphitheater when they added the show to WDW: less crowd problems, competing with the fireworks and not having to close the Mark Twain at dusk.
In retrospect, I feel if DL could do it all over again, they might have built a seperate theater for the show from the start, if room was available, a problem WDW, with their four parks, doesn't have.