I think that would depend a lot on your home layout and family or lack there of situation.
In my little house, it's just me and the dogs, If I'm downstairs, the living room light illuminates the whole bottom floor well enough and I can see pretty much the entire bottom floor from my favorite chair. My dogs bark if anyone comes near the front door, I don't imagine they would bark any less if someone scaled the gate into the backyard to access the window or backdoor.
If I'm upstairs, it's likely bedtime so I'd stay put and just turn on the light in there.
I would imagine unless you're asleep the sound of a door being busted in or a window being broken is pretty distinct. Unless you have family that needs to be secured, lights on or off, I don't think going searching for the BGs is a great idea.