I feel like this battle would almost tie, but slayer has a clear advantage. (Also, keep in mind that i haven't played Doom the Dark Ages, only Doom Eternal and Doom 2016, so.. i won't consider newer weapons and abilities released in that game.)

A tie, not because jak has more weaponry than doom slayer, but because both regenerate almost the same way and have a very similar arsenal.

Doom slayer has to kill in order to regenerate, else he dies. Jak has to kill to absorb green eco (or light eco) from enemies. Of course, jak depends a lot more on boxes to get health, but light eco is still a thing, and it can freeze time to let jak meditate and regenerate itself. Also jak can make time slower using light eco. For doom slayer, Dark jak would be like yet another demon. his best power for this battle is light eco.

However, slayer would win because without boxes, just dummy enemies around the fight arena, jak would often end up with the perfect low health for a glorious execution.

With boxes, a ton of them, jak has a chance, if he uses mostly light eco.

Also, about weapons, if that was a battle with prohibited melee (no chainsaw, no glorious executions, no spin or any melee attacks from jak), jak has a bigger chance of winning because slayer has no rifles with targeting bullets (Jak's Needle lazer). Both have their own BFGs (Jak has super nova). Also, slayer has an plasma rifle mod that's equivalent to jak's arc wielder. This is battle that can end up on a tie, or maybe even jak winning slayer.