Regarding the main topic of this thread, I actually do love Rent, but I'm going to have to go with Hedwig as the more satisfying, complete experience. Though I'd put American Idiot above both of them. :)"
I know that part of my love for RENT has to do with the memory of the first experience I had with it, a few days after it opened, with the original cast who was, to a person, so "in the moment" and passionate. Back then, it felt so life-changing, so present. Time and cast changes (and the awful off-Broadway revival) have changed my feelings into more of an appreciation for what it is and a wonder at what it might have been. (I know I'm in the minority here, but I loved the movie version.)
As for Hedwig, I'll be seeing the Broadway production a 4th time soon, and am really looking forward to it a lot. There are few shows I've gone back to so frequently. That said, Hedwig, for me, is one of those shows that is fantastic when you are there. A thoroughly satisfying show as you watch it. But I wouldn't count it among my favorite shows, and have no desire to listen to the cast recording over and over (I don't even own any version of it). And still, I go back...
I have to agree with kdogg36 about American Idiot - a show I didn't really care for the first time I saw it. But after going back to "see what I might have missed" the first time, and the 6 or so times I've seen it since, it is one of my favorites. I've never driven over 350 miles to see a national tour before or since, and I still listen to the cast recording frequently!