だろう is the plain form of でしょう, so its basic usage should be about the same. As it is plain form, it's naturally more masculine, since women tend to speak more formally than men in any given circumstance. That said, there are unseen determining factors that may influence speech patterns (background, age, rank, etc..) as well as personality that might come into play.
だろ sounds more like you're talking to yourself/don't care that your audience is listening.
The difference is:
何かあったのだろうか。- "I wonder what might have happened." (self-directed question) OR "Something must have happened."
何かあったと思う。 - "Think something happened."