As far as I can tell, the Georgain-era standard for sustained rate of fire (via the Duke of Wellington’s writings) for British infantry was 3 rounds per minute for a short engagement, which tells me that it would have dropped off considerably in a day-long battle. I suspect that the rate of fire from, say, Thirty Years War matchlocks (well after military archery consigned to the mists of history) was significantly worse. I’d be suprised if, after a full day off loading, firing, intermittently swabbing, and eventually scrounging water to pour down the barrels instead of drinking it, I’d be surprised if they managed a shot every three minutes.
That said, they could shoot all day, and we are talking about guns versus bows. I undestand Tokyo_Mann’s point about accuracy, because I tried archery myself when I was a kid, but there’s no way in hell I could press a real longbow as an adult even once, let alone for an extended period, but I can hit rifle targets just fine for as long as I have ammunition.
Which leads me to my last point concerning the superiority of the gun over the bow (and in the long run, everything else):
Aside from the fatigue factor (and I’m not saying that you won’t get tired shooting all day, you will) there’s another physiological advantage. For the first time in history, the effectiveness of a weapon did not depend on the physical strength of the user. A gun is just as deadly in the hands of a 90 pound weakling as it is in the hands of 240 pound linebacker. That’s not true of swords. Or bows.
Consider this: I’m a conscripted peasant who got about one day’s training with my musket, and I’ve just got it reloaded after a full day of marching, countermarching, shooting, reloading, etc. Here comes the enemy, Lord Schwartzenegger, who’s still mounted, fully armored, and equipped with a lance (maybe, it’s been a long day), a sword, maybe a mace if he’s extravagant, and a horse who’ll fight as hard as he will. He’s got to be fast, smart and able to survive, but I just have to get lucky.
And ther are ten more guys just like me right over there.