The correct answer is it depends.
First you have to understand the difference between strong and weak.
Making it short, a strong reference owns the object you are referencing with this property. What means that the compiler will make sure that this object will not be removed from memory while there is a strong reference to it. If you have two objects pointing strongly to another, and one is removed, the second one will still have this object, because it owns it.
A weak reference basically means that the objected is not owned, it's ownership is still from who has the strong reference, so in case the strong reference stop existing, the weak will be then pointing to nil. So repeating, A has a strong reference to X, B has a weak reference to X, if A removes this reference, B will lose it too..
So.. back to your question, weak or strong in the second View controller, it will depend.. is there a possibility that the first view controller will destroy the object while the second view controller is visible? If this happen you want to keep your copy of the object? If booth yes, put it strong.
If there is no way that the first reference is destroyed, or you want to reflect updates in the first object (updates keeping the instance) in the second view controller, a weak reference is enough.