I don't think there are enough Native North American bows from this period to be very sure.

Native North Americans made various types of bows, including longbows, shortbows, composite bows (combinations of wood, sinew and horn), and flatbows.

Composite bows were probably as powerful as those used by European / Asian steppe archers.

Longbows were not as powerful as European longbows, because the Native Americans did not have yew, which is a particularly effective wood for longbows.

Flatbows, on the other hand, are actually a superior design than the oval section of a longbow. Hickory and Osage Orange were often the woods used to make flatbows. Flat bows made of these woods might have been about as powerful as longbows made of yew.

Flatbows were harder to make, and took longer to make than longbows.

Most Native American archers used sinew for bow strings (some used Yucca string - Europeans tended to use flax or hemp string).

Sinew works well for bow strings when dry, but suffers more from damp than string bow strings.

I guess that the Native North Americans who used composite bows (Rocky Mountain and a few great plains tribes) and flat bows (North Eastern Woodlands) had bows comparable to European bows. Those (most of the rest) who used short bows or longbows had bows that did not match European fighting bows.

The North American Natives had nothing comparable to European crossbows.