I've stayed at both. Both hotels have small rooms.
Furnishings are a bit nicer at the Paramount and the lobby is alot nicer, but my biggest complaint is the height of the bed which is basically like a matress on the floor. The best part is that it is attached to Dean and Deluca which is a perfect place for breakfast.
The Milford Hotel is safe and a great location. The staff is nice and helpful. Depending on the room, they are often bigger than the Paramount rooms. If you are staying with a bunch of people, I would stay at the Milford because I saw four people crammed in a Paramount room, and it didn't look fun!
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?