There is one important distinction from what I've read: Spidermann is a spoof of Turn Off the Dark, whereas Moran's version is not intended to directly reference Ms. Taymor's version at all. He is doing what he thinks she should have done the whole time: Creating a Spider-Man musical that is loyal to the comics and actually has a good script and score.

I've already seen the slow motion train wreck that is Turn Off the Dark, and I desperately wish I was going to be in town for both of the other productions. Unfortunately, I'm out on the road...can't wait to see what people have to say about both other shows!