Fire arms have a certain shock and awe to them that bows lack, which give them a psychological edge in a battle. The first 'Gatling' style guns were nearly unusable due to the rate they would fail, however they were still deployed as they were scary regardless of functionality.
Guns also fair a bit better in poor (windy) weather and cut through obstacles more readily (especially in a jungle). Archers tend to be best in favorable weather conditions, which couldn't always be counted on in a defence scenario.
But the slow rate of fire of early guns made them inferior to bows in every other way.
This is only correct with an assumption...a gun is inferior to a bow in the hands of a trained bowman. Given to an untrained person, a gun is superior in pretty much every manner. Archery tended to be a lifestyle, especially in England, where a person would learn to use a bow in their youth and hone the skill over many years of practice. Raising archers for your army from a populace that had this background was a relatively quick process. However it took a significant amount of time to raise archers from a population that didn't have this cultural background. Reversely a standing garrison can be given guns with a little training and be ready within a month or two.
Should put a side note in that the Native Americans did in fact face 'armored' beasts. A gun was capable of dropping a Bison far simpler than arrows ever would and was a superior tool when used for hunting big game. Not all weapon acquisition was for war.