They do, or more accurately, they can.

It’s also important to distinguish what kind of bullet and what kind of arrow.

In general, a centerfire rifle round is a relatively small mass but high velocity projectile, and much of the damage it causes is a function of that velocity. Pistols by comparison tend to be heavier and slower bullets and thus are more survivable in most cases.

An arrow or crossbow bolt typically moves slower than a pistol or rifle round but with much greater mass. Still, any deer season in most locations will typically have three phases. The first is typically bow hunting only, the second is bows but muzzle loaders are also permitted, and the third is bow, muzzle loader, and rifle. It’s less a question of lethality than one of skill, as it’s typically much more difficult to stalk a large animal and make a bow kill than to sit in a blind or tree stand with a rifle. Bows are typically not useful the same range as a rifle, but a hit to the animal’s vitals is usually lethal.