I give this to Jack.
Dooku was particularly known for using a lot of
Force magic in his fighting style, including lightning but especially telekinesis. One of his greatest strengths was his ability to throw telekinetic strikes that even other strong Jedi could not avoid.
Dooku's style combined these Force attacks with the
Form II lightsaber style (he did not mix styles, unlike most other masters). This style focuses on footwork, balance, and economy of motion. The key to Form II is to use efficient parries to physically exhaust your opponent while manipulating the positioning and balance of the fight, then counterattack at a moment of weakness. Dooku used Force magic to throw his opponents off balance and integrated it seamlessly with this style. As a Sith Lord, he also mixed in
Dun Möch, a Dark Side method of combining Force telepathy with spoken taunts to anger foes and disrupt their focus (mostly effective against pure Light Side users, since they can't draw on anger for strength, which is why it backfired when he used it on Anakin).
If you take away Dooku's Dun Möch and all of his lightning, telekinetic strikes, Force chokes, etc., you are putting him way outside his comfort zone. He's still an extremely high-level sword fighter with mastery of all seven forms and years of dueling experience. But Dooku was an arrogant, preening man who believed passionately in the superiority of his unique methods. Every time he was overpowered or his style backfired on him, he retreated or lost. This effect would be even worse when, for the first time in his life, he had to face an opponent with a totally unfamiliar fighting style (since all Jedi and Sith drew from the same seven forms of combat from the invention of the lightsaber until the New Jedi Order).
Jack, on the other hand, fights new opponents all the time. He is highly adaptable and has a lot of perseverance. He is also fighting in his comfort zone, since none of his powers are restricted. As seen when he fought the Scotsman for 24 hours, he has enormous stamina, so
Form II will not be able to wear him out. His speed feats also exceed Dooku's, as
here where he easily deflects machine gun fire. Jedi use precognition to block one laser at a time, but they never block multiple lasers firing at machine gun speeds (several shots per second). This hand speed will give Jack an advantage.
Because of Dooku's cleverness, psychological warfare abilities, and years of experience, I will "only" give it to Jack
8 out of 10 times. But Dooku is severely hamstrung by taking away his offensive Force powers and pitting him against a new style for the first time ever, so there is no way he has the edge.