It was explained well by Gonzalo Méndez de Canço in 1600:
For war with the Indians no other armor except this is of any value. As for the coat of mail, the arrow could go through it and splinters of it would be very dangerous; the buffalo-leather coat designed to absorb sword-cuts is pierced very easily; and the corslet is very dangerous, moreover, if the arrow hits it will re bound and injure the next person. It is clear that the escupil [quilted cotton armour] is the best armor because the arrow is stopped by it and sticks.
(pg xiv, Jones, David E., Native North American Armor, Shields, and Fortifications, University of Texas Press, 2004, in turn quoting from pg 3, Evans, Philip W., The Arms and Armor of Raleigh's Roanoke Voyages, 1584-1590, National Park Services, 1997).
Basically, the armour choices were:
None. Light and convenient, but comes with a relatively high level of risk in battle.
Mail, which can be penetrated by splinters from broken arrows (which won't be too dangerous immediately, but the risk of infection was high), if not by the intact arrow.
Plate breast-and-back. This will stop any arrow that hits it. But it has relatively poor coverage. Arms, legs, lower torso (since it only protects to the waist) are unprotected. Also, as Méndez de Canço wrote, it doesn't actually stop the arrow, in the strict sense of stopping it, but will often deflect it.
Buff coat. Doesn't stop arrows.
Go native, and wear the local cotton or kapok quilted armour. It stops arrows and provides better coverage than a plate breast-and-back.
When the main threat was arrows, quilted cotton/kapok had a lot to recommend it. The armour they had brought with them was developed for the European gun-dominated battlefield, and would have been a better choice on the European battlefield. For a different threat in battle, different armour can be better. The key improvement was coverage of more of the body, compared to their own armour that would reliably stop arrows. (Not specifically for the conquest of the Inca Empire, but more generally when fighting natives; Gonzalo Méndez de Canço wasn't writing about the Incas - he was the governor of Florida at the time.)