I certainly wouldn’t say Nimitz didn’t make mistakes, that is certain.
Between the two, I am biased towards Nimitz due to his personal qualities and the way that he led men.
You look at leaders like Patton, Lemay and Halsey, and they were men who knew how to fight both with their brains and with their leadership. Of the three, I think Halsey was the least accomplished at using his intellect towards an end, he seemed to depend more on his aggressiveness and instincts.
Yes the Japanese totally snookered Halsey during the Philippines battles and it almost led to disaster leaving our landing forces unprotected.
He was saved by a few Destroyer Escorts and jeep carriers who fought so hard the Japanes were fooled into thinking they were up against a main force and withdrew before what would have been a major victory for them.