Great question — answering as the UphillTech team:
'Quick cooking' (aka 'instant') oats have been cooked more, and are in smaller pieces than regular (aka. 'old fashioned', aka. 'rolled' oats). If you'd prefer more texture in the bread, go with the old fashioned oats. If you're trying to make them less noticable, go with the quick cooking oats. If you only have one on hand, go with whatever it is that you already have.
Full answer by Joe: https://cooking.stackexchange.com/a/57549 (CC BY-SA 3.0).
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