While I agree with Chelley in principle, establishing your reputation in a new region is a delicate process. There's no harm in asking, you might think; and usually, you'd be right. If I were in your shoes, my decision as to whether to talk to Company A about Company B's conflicting better offer would be balanced by how much lead time there was for Company A to find a replacement for me; whether Company B's offer were an order of magnitude better than the Company A job; how connected the Company A people are to the theatrical establishment, and whether or not they hold a grudge.
Speaking from experience, it's a horrible feeling for Company A if they get left high and dry. But if your job with Company A is something like sound board op for four shows a week for $100, and Company B's offer is something like an AEA position for a mainstage show at Manhattan Theatre Club, that might be worth bringing up with Company A; particularly if you have a reliable, skilled friend who can take your place at Company A.
All I'm saying is that as theatre workers, our reputation is so much more important than our resumes in terms of getting future work. If you're trying to make a name for yourself in the cutthroat world of NYC theatre, I'd be extremely careful in making my first impressions if I were you.