I'm headed to New Brunswick for a June bear hunt. I'm taking my bow and a back up weapon. Which would you prefer: .270 win or 12 ga slug?

I have never been on a bear hunt before. I have never seen a bear in the wild. What do I need to know? How do you tell a big bear from a small bear?

My trip is planned for the last week of the New Brunswick season. Is this a good time to hunt for the big bear or should I be happy with whatever comes along? I want to have reasonalbe expectations, even though I don't have a clue what to expect.