I saw both last week. I am a huge fan of both shows, and in my opinion, both shows are in great shape. There are reasons to see both.
Here's the my opinion
Spring Awakening IS the hottest thing on Broadway--- to the tourists. I saw SA in January before the Tony awards, and the audience was far more enthusiastic and mature. This time audience members were laughing at things that were not funny, and it took away from the drama of the show. It is a very mainstream show now... However, the three principal actors are fantastic, and in my opinion, they make the show.
Rent - the audience is insane --- in a good way. If you love Rent, and Adam and/or Anthony, and you really want to see members of the original cast - you should go. This is probably the most enthusiastic and energetic audience you can see Rent with. It really is neat to see those guys return to their roles.
So, that was the Drowsy Chaperone. Oh, I love it so much. I know it's not a perfect show...but it does what a musical is supposed to do. It takes you to another world, and it gives you a little tune to carry with you in your head for when you're feeling blue. Ya know?