In meaning - yes, more or less. They can both mean that a person is difficult to please. In use - definitely not! The essential difference between this words is one of register, or in other words - the level of formality. 'Demanding' is a neutral word which can be used in most contexts, even formal or academic ones. 'Choosy' is much more informal word, mainly suitable for conversational contexts. The same goes for the words Shawn suggests - fussy and picky.

Yes, I believe they are. Demanding, fussy, picky, selective and particular are all synonyms of "choosy". Although demanding can mean other things too. For instance, 1. requiring much time, effort, or careful attention a. The demanding art project kept them up all night. b. The demanding requirements of the Computer Science department deter many students from taking the major. 2. hard to please -- I think this is the one matches up with "choosy". :) c. He won't perform for an audience that demanding. He'd rather play guitar just for his friends and his family who all love his music. 3. requiring considerable physical or mental effort d. The demanding task of grading student essays often gives me a headache.