Slower burning powders, when used in the proper cartridge, are effective by performing more work on the bullet by means of more pressure throughout the bullet travel down the bore. More pressure at the muzzle exit usually means there was higher pressure behind the bullet there. That also means the gas velocity will be higher - maybe 4,500 fps vs 3,600 fps for the same cartridge. A larger diameter bullet requires less pressure to be accelerated to the same velocity as a smaller diameter bullet of the same weight.
The sudden expansion of that gas plume is what produces the "bang", just like lightning produces thunder. The bullet itself is also producing a shock wave, if it it traveling faster than the speed of sound. You can hear the noticeable difference between a .22-250 at 3,600 fps and an 8x57 at 2,600 fps, due both to the gas velocity as well as the bullet velocity.