Neither of them will die because 1) The plot is forcing them both to live in order to end the reincarnation cycle (if they succeed in bringing peace and working together, the hate cycle is stopped.) 2) The Last is cannon whether you like it or not. They both are in it. It takes place 2 years after this whole war arc and not in some alt dimension of "what could of happened". It even has Sasuke with his sharingan/rin'negan eye to prove that it's sticking to cannon!
So there you go, no, they don't die.