Strength:
In terms of physical strength, Jack Sparrow seems to have the upper hand, simply because he's literally got the upper hand, while Hook has his eponymous hook. (Two functional hands are arguably better than one, as we learned from the ending of The Last of Us Part II.)
That being said, in spite of his lean and uninspiring frame, Hook exhibits immense physical strength, so much so that he has strength enough to pry open a crocodile's mouth with his legs. Sea-leg day is important for pirates.
Dexterity:
Jack Sparrow has the definite advantage here. In every fight, he moves with frenetic, almost ceaseless, energy. However, in his freneticism, he tends to not look where he leaps, which leads to him being quickly knocked out of a fight (see: taking a metal bar to the face during the three-way water wheel duel).
Hook's fighting style is more polished and refined; every step he takes is methodical. He fancies himself a gentleman, and would find Sparrow's jumping and dancing around to be a clear case of "bad form", completely beneath him.
Constitution:
This is a major toss-up; Jack Sparrow and Hook are essentially human. There is nothing particularly special about them at first glance.
That being said even as a human, Jack is pretty durable and is easily able to shake off injuries that would incapacitate most men, from being slung about by a rigging blowing in a maelstrom and hurricane force winds to smashing through a series of rope bridges in a hundred-foot fall from a mountain.
Captain Hook? He's been able to fight off a crocodile, even while in said croc's jaws. He can also hold his breath for extended periods, as when the croc pulls him under the water, only for him to emerge later.
Intelligence:
Jack Sparrow can be clever when it comes to thinking on his feet; very good at improvisation, and better at tactical thinking than Captain Hook.
As an attendee (graduate?) of Eaton College (I'm considering it canon, despite not being mentioned in the Disney film), Captain Hook towers over Sparrow in terms of sheer intelligence and planning.
Hook is a strategist; he may lose a battle, but that loss is only momentary while he regroups for the much larger war.
Needless to say, if Hook and Sparrow were playing chess, Hook would be the decisive victor.
Wisdom:
And here's where I go into full-nerd mode. In order to better differentiate between "Intelligence" and "Wisdom", I turned to the D&D stats.
Using D&D's metric, Jack Sparrow would rate at 14-15 ("Can get hunches about a situation that doesn't feel right").
However, Hook outclasses him here at 18-19 ("Often used as a source of wisdom or a decider of actions")
Why would I say this? Jack Sparrow has a history of being mutinied against, from Barbossa leaving him on a desert island (twice), to Elizabeth chaining him to the Black Pearl's railing as squid-bait while everyone else got the h-e-double-hockey-sticks out of Dodge. Nobody sees Jack as a competent or capable decision maker.
Hook? Zero mutinies, and has a crew that genuinely respects him as a leader, even if they are somewhat sycophantic in that respect (Mr. Smee being the perpetual yes-man).
Charisma:
At first glance, Jack Sparrow would be the de facto winner in Charisma, simply because Jack Sparrow is essentially an exaggerated version of Johnny Depp (blended with Keith Richards), who is naturally charismatic in real life.
Hook, on the other hand (the un-hooked one), has traditionally been portrayed as an exaggerated version of Mr. George Darling (father of Wendy, John, and Michael). As such, whereas George Darling was a stern curmudgeon, Hook could be downright sinister, as a caricature of the domineering father figure.
Once again, going to look at D&D stats. I would put Jack Sparrow at 20-21 ("Life of the party; able to keep people entertained for hours"). He's a high-seas playboy, always looking for the next big score, be it a bank vault or a colonial bureaucrat's wife. However, once those hours are over, there typically isn't much left. He grates on people, especially when those people are ready to stop partying and be serious. We see this in the shade Gibbs throws his way during and after the court breakout. Even Jack himself was prone to being sick of the shenanigans, as we saw him shooting and killing a hallucinatory clone of himself in Davy Jones' Locker ("Gentlemen, I was my hands of this weirdness!")
Hook beats him handily (hookily?) at 24-25, "Renowned for wit, personality and looks".
Hook styles himself as a blue-blooded gentleman, and conducts himself accordingly. He prefers to negotiate to get his way rather than turn to a straight fight, as he does with Tinkerbell in order to find the Lost Boys' hideout.
Even outside of negotiation, this attribute is especially shown in his clothing; his dress is always finery from silk shirts and frocks to his elaborate red overcoat. He even forgoes the much more practical common boots worn by most seamen in favor of the stockings and heeled shoes of English nobility. Also notable is that he takes great pains to maintain his physiological appearance, having first mate Smee act as his private barber, and keeping his moustache well waxed.
He holds himself to a higher moral standard (aside from his yearning to murder a child...but in his defense, that child DID cut off his hand and feed it to a crocodile), and sets himself as the example to which his crew should aspire. The closest we see to this in PotC is in the form of Hector Barbossa (and to a lesser extent, Blackbeard), however Captain James Hook, in all his blue-blooded snobbery, would be downright APPALLED at such a comparison.
Weaponry:
Jack Sparrow armed with a rapier and pistol with only one shot.
Captain Hook armed with a rapier and his signature hook.
Freak Out Factor:
Jack Sparrow has a crippling fear of death and will quickly turn tail and run whenever something threatens to end his life, doubly so when that threat is of supernatural origin.
Captain Hook is easily driven to madness by the sound of a ticking clock combined with his PTSD-infused Herpetophobia (fear of reptiles)
So what say you?