Well even decades after canons and rifles were introduced to European kingdoms, their armies still used traditional medieval tactics. Pikes, crossbows, swords and bucklers.Because muskets were unreliable, ammunition was hard to come by, and while a line of musketeers were reloading after firing their first volley the archers they went up against would still be raining arrows on them.
It would be until the invention of things like cartridges (paper or metal), breech loading guns, and more potent forms of gunpowder that firearms would dominate battlefields. If you took a line of 16th or 17th century riflemen against longbow archers. Chances are that the longbow would have the upper hand because it has a longer range, better accuracy, and could be shot at a faster rate.
The only upper hands that early muskets had was that you could take any chicken **** settler or peasant and train them on how to use this weapon in a matter of weeks. Archers on the other hand takes years of training. Welsh longbow men from the 100 Years War had to be trained from boyhood on how to use yew bows long before they would be deployed to France.
After all, muskets were as primitive as firearms get. Napoleon's armies had cavaliers who were armed only with sabers, during the Mexican American War American and Mexican cavalry soldiers were still using things like swords and lances as well. There is a reason why those old rifles had bayonets attached to them.
This all changed after the 1860's and 70's when cartridges and shells came about. Suddenly soldiers could fire at faster rates with carbines or cartridge rounds. This is when lances, bows, and the like truly became outdated. Its easy to attack you opponent if he's spending half a minute loading up a single shot after all isn't it?
So yeah, guns may be much more powerful than bows but don't let anyone convince you that bows are not deadly. All you have to do is look at history. The Mongols carved out an empire that spanned two continents with horse archers. Welsh Long bowmen who fought on behalf of England during the 100 Years War were known to lay waste to lines of heavy French cavalry, these yew bows were so strong they could penetrate steel armor.