Seeing as how Korra is an avatar she is capable of bending the four elements Earth,Fire,Water & Air she is very adapt at using each element because she has been trained sense childhood. Korra can also enter the Avatar State. While in the Avatar State, Korra is able to use an air spout to raise herself into the air while unleashing all four elements in rapid succession. Later after more training, Korra becomes able to easily enter this form with complete control, even during intense competition.
Kakuzu, like Korra can use several elements at a time them being Fire,Earth,Earth & Lightning due to the hearts he has taken from fallen enemy's. Kakuzu has th unique ability to live as long as he has hearts.(5, four in each mask)
Kakuzu also has the unique ability called Earth Grudge Fear,
The Earth Grudge Fear is a secret kinjutsu of Takigakure which transforms the user's body into something similar to that of a rag-doll's, which is held together by hundreds of thick black threads
This allowed him to separate his body parts at will, to perform long-range physical attacks and sew up almost any injury he suffered.
Land of Lightning's coast
(Where edo Kakuzu,Ginkaku,Kinkaku,edo Asuma's battle all took place at.)
Both combatants start off in there base form, this is living Kakuzu(5 hearts)not edo in case any of you where wondering.
I will be giving this match to Kakuzu because he is 91 years of age he has far more battle experience then Korra does. Not to mention with his tendrils he can close the gap between himself and Korra in battle in order to restrain her he could make an opening to use a mask(s) elemental affinity and cause a fatal blow to Korra.