Unlocked is safer. You are much more likely to have a medical emergency than experience a break in. In a medical emergency every second counts. Imagine how awful it would be if you could hear your child having a medical emergency but you cant get in their room because their door is locked.
If someone breaks into your house, they either will try not to wake you up and never attempt to get in your room, or they definitely will get into your room and one more lock will do nothing. Lock your door if you want privacy from people who could otherwise access you, but if someone dangerous is already separated from you by at least one lock, adding another doesn’t help.