You can't compare Chicago to Moulin Rouge, because they share, really, nothing besides the fact that people sing and dance. Moulin Rouge stands alone. I really love this movie.
Nicole Kidman did sorta over act in parts (the Elephant scene, and when she tells Zidler she wants to leave.), but other than that, the acting is wonderful. I just love Ewan McGregor's character, and I love Ewan McGregor. John Leguizamo's character, Henri Toulouse Lautrec (yes, the famous painter), I found was just such an annoyingly funny character, he was definently one of my favorite characters. The Duke (Richard Roxburgh) is definently overacted, and frankly, Zidler (John Broadbent), is sooooo horribly annoying, you really would want to throw yourself off the Moulin Rouge windmill.
I love this movie. There are some funny parts, but they are mostly just in the beginning, and the best musical number isn't 'Diamonds', but rather, the dramatic 'Roxanne'. Another one of my favourite pieces is 'Nature Boy', the song sung at the very beginning. It's so sad, but very touching.
The beginning is sort of depressing, but it doesn't last long, so don't stop the DVD then. The middle sort of drags on, so be warned. The sets and costumes are beautiful, and very colourful, and the dancing is really Spectacular Spectacular (excuse the pun...), but long periods of time with the Bohemians, or at the Moulin Rouge can make you feel like you're stuck in a circus tent. But since Ewan McGregor's in it, I give it 10 stars.