You do not know the intent of someone that has invaded your home.
Is your life or your family's lives worth taking a chance to find out?
You are taking the chance either way. You can start with an assumption that this is a normal and typical B&E, where the perp is after property, or you can develop some other idea. But working toward the greatest likelihood is a pretty smart path. As for the lives, why do you think that starting a gunfight will be safer than giving the BG a chance to leave without a fight? It's amazing the number of people here that think just because they are the goodguy that they will always win, and there won't be any ramifications. If he doesn't leave, you can go to guns, but to start with that option closes down any other alternative.