Okay, so let's start with their AP.
Samurai Jack should have AP comparable to his durability, which averages out at 1.57 kilotons of TNT and goes upwards of 3.87 kilotons of TNT.
Hyodou, on the other hand, has a consistent AP of 3.07 kilotons of TNT, but that was for his second key while his 3rd key implies that he's far stronger than before.
As for what they can do, well... Samurai Jack does have a counter for astral projection according to this.:
- Astral Fighting: One time his soul was sucked out by a demon, but he proceeded to fight inside of the demon with just his soul and defeated it, freeing his soul and all of the other victims of the demon back into their bodies. Jack used a similar ability earlier to enter the dimension within Demongo's body and release the souls he amassed.
So that isn't going to be too much help in Hyodou's favor.
Hyodou's rage power is just going to screw him over because having seen Season 5, I know Jack only got his sword back after quelling his own hatred and thirst for revenge. With hatred being a clear marker of evil and Jack's sword being able to damage AKU of all things, Jack has a hard counter against Hyodou in that regard. Hyodou's Empathic Manipulation justification is as follows "Can write a charm that induce tranquility and peace in his or someone else's mind," but I dunno if that'll hard-counter his hatred or not. Someone who knowledgeable about Sengoku Youko will have to fill me in on that one.
Not sure how Jack can counter Hyodou's Attack Reflection or even his Instinctive Reaction. Instinctive Reaction is a pretty out-there form of defensive and offensive ability, so much so that even inexperienced users like Goku on his first UI Omen or less powerful users like Anne Boonchuy can pull off outstanding feats with it.
The way I see it, Hyodou letting his hatred get to him will be an instant win for Samurai Jack, but in any other scenario, it's likely Jack will need to call upon his ancestors in order to handle Hyodou in what would otherwise be a fair fight.
I'm not gonna vote yet as this looks like a match that needs more debating.