In short: literally everything except ease of acquiring ammunition.

Some Roman ballistae excepted, trebuchets and other counterweight or torsion-based engines were not really battlefield weapons in the way that field artillery would become. That is, they rarely, if ever, were used tactically against troops in the open. They were big, heavy, had to be broken down to transport on carts, and just didn't do a hell of a lot against individual soldiers. They were really more attritional siege weapons, which, over a long enough span, could batter a wall into disrepair or demoralize a garrison into surrender. But you'll be hard pressed to find more than four or five major sieges that were won entirely, or even primarily, by chucking rocks at the walls. Saps - that is, digging under the walls and collapsing both the tunnel and the wall above it - and storming the walls with ladders/belfries/subterfuge were more common, and waiting the garrison out was more common still.

The earliest cannon were not really ideal for open field fighting either. They were used as such at times, because cannon are bloody terrifying and far more effective and longer-ranged than trebuchets et al, but it wasn't until the 17th century that cannon mobile enough to keep up with advancing troops came into use. Prior to that, they were more or less parked at the beginning of the battle and stayed there. Cannon improved vastly over the next two centuries, and it's not really fair to lump them in together. A Napoleonic battery was far more mobile, lethal, and versatile than one of Gustavus Adolphus's light batteries, or even one of Frederick the Great's.

Rather, cannon were siege weapons par excellence. The difference in destructive power, not to mention range (always best if the defenders can't shoot arrows/muskets at you while you're shelling their teeth loose) can hardly be overstated. The introduction of cannon to siege warfare prompted major and almost immediate changes in military architecture in a way that no medieval weapon really had. A tall, narrow castle wall that would have taken trebuchets weeks to bring down - if they managed it at all - would be a rubble-choked breach after a few days of serious cannonade. Defensive walls had to be built low and immensely thick if they were to have any chance of standing up to such a battering.

To add onto u/Rittermeister's answer a little bit. During the 14th century guns often were more of psychological weapon than anything. Something like the loshult gun would have been fairly portable and likely penetrated armor assuming it hit anything, but gunpowder was expensive, unreliable, and guns typically weren't fielded in large enough numbers to have much of an impact. Accounts from the battle of crecy claim that the English guns there were mainly set off to scare the French crossbowmen. We also have examples of sieges where dozens of cannon were set up around a town, but only a handful were actually fired due to the cost of powder.

Towards the end of the 14th century new methods of producing nitrates significantly reduced the cost of gunpowder and greatly increased the use of gunpowder weapons. There was a lot of experimentation with field artillery in the form or multi-barreled ribauldequins and simple handguns, similarly many castles were being built or modified in order to accommodate small cannon and handguns for defense. On the offensive side, engineers compensated for the relatively weak nature of serpentine powder by going bigger, resulting in a period of larger and larger superguns. Even an extremely large trebuchet which can throw a 90 kg projectile 300 meters just sort of pales in comparison to a large bombard which can throw a 300 kg stone ball 1000 meters and smash the strongest walls in Europe. The main downside was that these were fairly difficult to move and had an extremely slow rate of fire.

Towards the end of the 15th century the cannon started to gain it's "classic" appearance. New casting techniques allowed the creation of lighter, longbarreled guns built to use more powerful corned powder. These guns could achieve a much higher muzzle velocity, much better accuracy, and cooled much faster allowing for a much higher rate of fire. This meant that rather than relying on a single massive stone, the same devastation could wrought by multiple lighter cannon repeatedly pounding the same location with iron cannonballs. By this point there really was little reason to use anything but cannon.

Bert Hall Weapons and Warfare in Renaissance Europe

Tonio Andrade The Gunpowder Age