In Wild Talents, 2nd edition, the widest attack roll goes first, with ties going to the taller roll. I'm confused and haven't been able to find any information on this in the book: if two people roll an attack action with the same Width and Height, who goes first? Do they go simultaneously? If they go simultaneously, I assume their actions would resolve before wound penalties applied, and they could potentially kill each other. If one has to go before the other, it couldn't be determined by re-roll (due to pure hard dice rolls).
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Wild Talents doesn't mention this anywhere, which is an oversight, but ties are an expected feature of the One Roll Engine. When a tie happens, it's exactly that: a tie. I can't find the reference right now, but I distinctly recall reading Stolze's response to the possibility of ties in ORE being a virtual bemused shrug and the instruction to resolve ties as seems sensible. Your intuition that damage is applied to both combatants before wound penalties are applied to their rolls is definitely sensible.
Note that not every competitive roll is a going to be tie-able. There are two kinds of competitive rolls, outlined on page 29: contests and opposed rolls. In opposed rolls, one is trying to act and the other is trying to stop that specific action. The mechanics for opposed rolls aren't rolls higher or wider, but rather whether the first character's roll can still succeed at the task after the opposing character's roll removes dice from the first's roll. This isn't the typical kind of roll used in combat (unless you're actively blocking/dodging/nullifying an attack: page 75, "Defending is always an opposed roll").
Attack rolls are an example of contest rolls. In this, the rolls are not directly opposed to each other, and it's possible to have ties. Everyone who ties resolves at the same time, and then everyone who was slower gets to act after those wounds and effects are resolved. Attacking an unfamiliar opponent without holding back dice for a simultaneous block is risky!