Thats actually a really good observation mate...
Heres what I think: A newborn Soul is naive and blunt. It doesn't understand between good and bad deeds. That newborn soul doesn't have any emotions. It might commit a crime and don't feel anything about it. So that's not really a Soul. Soul gives us the power to feel things, to feel emotions so A NEW BORN SOUL is not really a soul, but just an entity. So till the death of the vessel, the entity gains enough knowledge and is matured enough. And now when the same entity takes another birth, it knows whats wrong and right, it feels things now.

So I would say, Death comes first...