I don't think there's any official ruling as far as this situation is concerned in AW. At least from all of my searching when this came up there were not.
What I did find was:
That last one is important- it informed my take for my world.
My original take was to have both roll simultaneously, and look at both rolls when narrating the results. That approach worked, but it was ultimately unsatisfying.
My final take when I went back to the drawing board was to make use of hold to only deal with the initiative. Then use the standard approach- including my first take.
When two characters are duelling to the death,
Answer the following questions for your character. The MC will answer for any NPCs.
Are you ready to die? If yes, hold 1. If any player doubts your word on this, say what you will to convince them. If they still doubt you, don't hold 1.
Are you free of remorse or hesitation to kill? If yes, hold 1. If any player doubts your word on this, say what you will to convince them. If they still doubt you, don't hold 1.
Are you completely calm within yourself, free from self-doubt? If yes, hold 1. If any player doubts your word on this, say what you will to convince them. If they still doubt you, don't hold 1.
Whomever spends the most hold goes first. Unused hold can be used to increase the die roll by one on your attack. If both players spend the same hold, they make their rolls simultaneously, and both outcomes are applied.
It worked well. And it also made duels as epic as I'd wanted to make them.