The longbow fired a longer projectile, so there was a longer acceleration period.
However, it was only a strip of yew. Look at the "Cupid's bow" shape of the compound bow. This had a far more curved body, and fired a longer arrow. Compound because it was made of sinew and bone as well as wood, in laminations. The advantage was it could be fired from horseback, as it was shorter from top to bottom.
But the cross bow fired a shorter projectile, the fletched "bolt" for hunting with the "arrowhead" tip, and the quarrel, solid wood flights and body, with a pyramid shape, tapering to the rear, and pointed at the front.of often solid bronze.
Hunting crosbows were often a single wood arc like a bow, and were cocked by standing in a stirrup at front and pulling the string over a sear (hook) connected to a trigger at the back.
But the queen of the battlefield was the compound crossbow. The arc was often steel or wood, sinew, and bone laminations, and could be 4-6 " thick at the centre.
This is a da Vinci
showing the Bow at the peak of its development.
For a bow this powerful, you cocked it either with a windlass
Problem here is too much cord, getting damp and slack in rain. Note when the cord goes back a certain distance, it is held by the sear and then the windlass is removed ready to shoot
Or you cocked it with a crannequin
Which is like a car rack and pinion steering mechanism. The hook on the right would hold the cord and brace it back while it's being wound.
In use you aimed directly as with a rifle. The cross-bow was slower firing, but far more accurate. And you could train a crossbowman in a week.
Think if you like of the volley firing musketeers and the pinpoint slow shooting riflemen of 2 centuries later. And boy! That quarrel was a real armour piercer.
Compared with the Red Indians' our bows were far more lethal. They had to riddle their victims to bring them down. Sorry terry.