Dooku is faster and more skilled and seems to enjoy landing kicks on Obi-Wan as well.
In the all-out round, he has the benefit of considerably greater Force power as well.
Dooku wins the first one about 8-9/10 in a good fight. Kenobi's Soresu lacks the means to properly counterattack, and Dooku has encyclopedic on Kenobi's Ataru, which makes it hard for Kenobi's attacks to do much. Dooku wins every time in the all-out round.
Dooku was capable of fighting off both Obi-Wan and Anakin together in RotS, and Anakin was the only real issue. In TCW, Obi-Wan was still no challenge and he was repeatedly saved by Anakin, and that was without Tyranus using his offensive Force powers.
Naturally, Obi-Wan is formidable enough to make it a good fight. Obi-Wan's forms and styles are just inappropriate for the likes of Tyranus. His Soresu form lacks the offensive capacity to land a hit on Tyranus, and Dooku knows Ataru extremely well because he has fought Yoda several times and sparred with Qui-Gon countless times. That leaves Kenobi with practically nothing to efficiently attack Dooku with, so all he could do is defend himself, which he can only keep up for so long before the Count lands a telling blow or disposes of him through the Force.
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