Damage wise should they not be fairly closely matched given both have passives boosting damage? The core of the matter lies with weaponry where i do believe slayer is superior in terms of offensive power.
Far stronger? That´s only with a conc pot and the double stab at which point you give up the sweep which is a huge downgrade to fighting large groups.
…what? This depends entirely on the disablers.
Both of them are weak to assassins, hooks? Slayer is better against hooks since he can just jump into them (immune to the grab if he starts it before they do) and both are weak-ish to leeches in a horde.
If you got multiple hooks in a melee horde then the only time GK is better is when he has the sweep ability but then he doesnt have boss damage. If he doesnt have boss damage then slayer is overall just better unless dealing with gunners.
But neither of them is really good against gunners, not even GK with a shield, he just survives if they come in close by.
Potions are nice, but his other blessings are RNG and arent reliable at all. You can get regen and power which is hella strong but you can also get 6% attackspeed and 10% damage reduction which does almost nothing.
Slayer meanwhile? By having two weapons he doesnt have any enemy type he is weak against except gunners. With leap + crunch spam he can stunlock hordes without a shield, even elites inside the horde and he wont feel much pressure even when dealing with a lot of monks.
He can deal with just about anything that isnt a chaos warrior + horde pretty quickly&safely that is.
The only time i´d really want GK over slayer is when i really want to burst bosses with the double stab and the team is strong enough in melee to not need a GK with the ability to to burst an enemy elite frontline.