Kankurou
1. Sasori Puppet
2. Mother and Father Puppets
3. Black Secret triple threat
4. Poison weapons
Kakuzu
1. Greatest amount of combat experience in the Narutoverse
2. Doton: Domu creates a Diamond hard skin that is virtually impenetrable unless attacked with lightning
3. Katon: Zukkaku attack that destroys ones footing...Area effect
4. Raiton: Gian move creates bolts of lightning strong enough to push back dual raikiri. Can target multiple opponents
5. Jigongu black threads create for ambush from underground and increased reach
6. Supreme taijutsu...man handled Kakadhi with a MS level sharingan
7. Five lives
8. Fuuton Asugai creates an extreme wind blast. Area effect
9. Fought and survived Hashirama Senju without Earth Grudge Fear
In combat, Kakuzu and Kankurou are equaled out in terms of deployment...meaning they roughly have the same number of puppets and masks; however, this is the real problem.
Doton: Domu trumps Kankuro's entire arsenal...furthermore, his masks lack blood other than the protected heart so Poison is virtually useless. His black secret formation can do nothing because of Domu and his Jigongu threads. The Sasori puppet head only a fire pump which is tanked if not pushed back between Zukkaku and Asugai combined. The mother and father puppets get now where just like the black secret formation...they are more symbolic than combat oriented.
Additionally, the more puppets Kankurou deploys, the worse for him. He has to work at controlling the puppets while trying to attack and dodge Kakuzu. Kakuzu on the other hand operates with sentient Masks that act on their own or on his command making him more efficient in battle.
Kakuzu wins in my opinion.