'Are you coming' implies previous knowledge of the topic and that the respondent has considered his/her decision. 'Will' implies that this is the first time the question has been asked.
Neither are best...depends on whether the topic has previously been mentioned..
I agree with what has been said about the difference between "will" and "be going to" to express future time. However, I think that the use of a conditional clause changes things a bit. Suppose you're the speaker -the one who is asking the question. If you haven't made up your mind yet about going to Chicago, how can you ask me if I'm going with you or not? In my opinion, the main reason wh