Dooku is pretty much superior in every regard.
Sure, Ulic has some neat advantage within his combative manner; Djem So's stylistics, incredible physical force, on-par speed, wonderful offensive onslaughts and such, but comparing them overall in their dueling skills and capabilities, Dooku is a notch higher. Ulic's stylistic advantage isn't enough to make up for the general gap between them.
I doubt Force power comes much into play. Dooku is leaps and bounds above Ulic in power output within offensive displays, is incredibly masterful in Force usage mid-combat (unlike 99% of characters), but Ulic's defensive applications are on par with Dooku and it can be inferred from theme that Ulic holds enough Force connection to trump most of Dooku's attempts with direct Force attacks.
Still, an great fight.
Interested to hear why, is he going to outfence him? Something can definitely be said for Dooku's mastery of Makashi but I can't see it taking a win over such a physically imposing and masterful swordsman. It definitely gives Dooku the experience to duel him for a long time.
Therein lies the problem though, the longer the duel drags on the stronger and more powerful Ulic gets. Dooku hasn't got the same luxury, he isn't tiring quickly by any means but Ulic is only going to get more formidable and harder to deal with.
Dooku can't take him through Force like he does to Anakin either, Ulic is a real tank defensively with the Force. Dooku has to win quickly and I can't see that, especially with Ulic's notable durability as well.
Pure sabers Dooku can't really generate enough kinetic energy against him, and Ulic will literally keep him on the defensive and eventually tire him out. This guy didn't have his defense smashed in by Exar smashing through Beskar Kun, and is just too relentless to allow the Count to exploit a weakness in his defense.