I think you've missed a third option of how this happens. And it's the most likely.
In the show, Bran is trying to change the past. BR stops him, but now he's gone.
We know that he can warg into people
during his visions of the past, but that everything he does only results in things playing out the way they were meant to. "The ink is dry."
The logical solution then is for Bran to travel back in time trying to change things in the past. Each time he fails, he travels further back the next time.
Ultimately you'd think Bran would try the most straightforward thing, travel back to the moment the WW were created and attempt to prevent their creation in the first place.
Of course, he can't actually change things. So things play out the way they always have.
Bran thinks he's friends with the Children. But 8,000 years ago he was not, in fact the children were at war with Men.
He attempts to warg into the man we saw in s6e5 and reason with the Children. Instead they sacrifice the man tied to the tree in an attempt to create a weapon.
Unbeknownst to them, the worlds most powerful greenseer is inside of this man. That's how the weapon turns against the Children, and that's why he can seemingly warg the dead.
Driven by a hatred of the Children for cursing him to an icy immortality, Bran/NK wants just three things:
- He wants to eliminate the Children, the people that betrayed him.
- He wants to see his home and his family again.
- He wants to finally die after 8,000 years.
So the Wall comes down and the WW reach winterfell. Bran/NK is finally home.
Meanwhile, the Bran that we know probably hangs out on the isle of faces with the last Children. As Jon/Dany clash with the WW, Bran/NK is reunited with his brother (cousin).
Bran needs to take his own life to save his family, because the WW don't exist absent his presence in the Children's sacrifice. Simultaneously, Bran/NK wants the same thing. He knows that if he kills our Bran, he'll be released from his icy prison, because he's really killing himself.
The ink is dry must play a factor somehow, as must the bittersweet ending.
I would bet that Bran is simply destined to become the NK, and nothing he can do will stop it. And so In the end he will become the NK. But Jon will prevail in the battle against him, unknowingly killing his own brother.
Honestly it seems like the show will almost certainly go this route.
don't ask me how)
and they have the nerve to talk about honor 
to their whole crew (excluding Halfman 
) but every scene they're involved in is top notch. I kind of even miss Joffrey 
- the way Tywin used to son him was 
All you got left is a mad Queen and One-Handed Simp
need to rewatch season 6 this week
