Hmmmm. Was listening to a podcast just this morning on Henry Hudson and one of his crewmen was killed while on a survey party around Manhattan, an error shot from a canoe, got the crewman right in the neck.
Both were skilled, but Native Americans had to hunt; medieval yeoman shot for distance.
I believe the English longbow in the hands of a skilled archer would have a considerable edge over the best native American weapon wielded by his counterpart here. A crossbow would be so overwhelming in superiority that there would be no contest.
When I think medievel, I think a rushed sort of raging war. Arrows blackening out the sky. The soldiers/knights were numerous. The Indian though, has a skill for blending with nature and having patience.