Hmmm. Well since you live in NYC, I would recommend Put your main bass in so that it's the one against your body, and your backup bass on the 'outer' side so that it will protect the main bass in the inevitable eventuality of gunshot damage.
That way your best bass is protected and so are you if you are attacked from behind by a random thug. And if you are attacked from the front only the backup will be damaged when you collapse backward onto your gigbag. So that way, your surviving family members can sell your good bass to pay for the funeral.
What? Oh I suppose you're going to try to claim somehow that New York isn't the festering cesspit of crime that movies, books, and the evening news make it out to be.
Okay. Smart@$$ moments aside: Keep your better/main bass closer to your body so that things like leaning against surfaces will have less effect. Both basses should be fine regardless, but any sudden lurch can make someone fall against you and kind of 'smush' the bass a bit. I wouldn't think you could absorb much in the way of real 'damage' that way. But I could sure picture needing to re-do your set up afterward.