Umm no.

Let's take a look at a few facts. An English Longbow, using information from the bows recovered aboard the wreckage of the Mary Rose had a draw weight ranging from 100-185 pounds. So some bows were around the 100 pound range, while others could top out at 185 (likely quite rare). Being charitable, let's work with a 150 pound draw weight.

Now, a variety of English arrowheads have been recovered, and many of them are around 905 grains in weight. Using this handy bit of information we can determine that a 150 pound bow could shoot an arrow at around 250 feet per second. Taking that information and plugging it into a kinetic energy calculator we learn that this 150 pound bow shooting a 915 grain arrow generates about 127 foot pounds of energy. English longbows were not accurate past about 400 meters, and Henry VIII set a minimum practice range of 220 meters for adults.

So, presuming the data and sources for the wiki article on the English Longbow I drew most of my technical information from is correct, or close enough for government work, we can move on to the much more interesting (to me) Civil War musket.

Using the .58 Springfield as our counter to the English Longbow, we are looking at a rifled musket shooting a 500 grain .58 lead bullet over 65 grains of black powder. Using this handy table which agrees with what I've read and understood about the 1855 Springfield, we see that it shot it's 500 grain bullet at 950 feet per second, and generated about 1000 foot pounds of energy.

Compare this to the 250 per second of the long bow, and the 127 foot pounds of energy developed. The rifled musket was accurate to 500 yards in trained hands, which far surpasses the accuracy of a long bow.

Even if we go back to smoothbore muskets, a .69 smoothbore is accurate to about 100 yards, and still generates far more energy than any bow, and with a fraction of the training.

Guns were used in place of bows because they were easier to train and operate, and much, much, much more powerful. The initial high rate of fire they offered wasn't much more than the rate of fire of a trained soldier with a functioning weapon.

Tl;Dr, boomstick > bows and arrows. Didn't we learn that lesson from Ash already?

That depends on what you mean by superior, you could achieve a higher streangth with a crossbow or rifle, but it didnt have the same rate if fire.

A longrifle had an effective range of over 2oo yards with a competant user. With a sustained rate if fire of a little over 2 per min

A longbow also had a range of more than 200 yards, and a rate of fire of around 6 a min for sustaned fire

However the rifle has higher penetration and "stopping power" than does a longbow.

The english longbow was undeniably an effective weapon in the hands of an experienced user. And, disregarding the training required could justifiebly be called the best in the time frame given

The rifled musket is in a grey area here, in terms of performance it blows the bow out if the water, with an effective range of more than 450 yards, however it was used during the civil war, on the other hand it was also a muzzle loader, so I am unsure if it counts for this question

I am biased, both in the favor of Early Modern Warfare but also against the English, but I would say the musket Iis superior. It has more to do with costs and training time. The time needed to be an expert at a longbow is a life time while a recruit can pick it up in a couple of weeks. So in the lifetime needed totrain a few hundred archers (all individually trained across England) I ccould train a corp or two of fusilers . In respect to training time to use, more men is more effective.

Well, the problem is it's not clear what's meant by "superior" in this context. Every weapon has unique costs and benefits that allow it to function in at least some sort of niche - there's no universally superior solution.