Not as such. It reflected more the difference between the two men and their style of command. Halsey was much more of a gambler, far more aggressive than Spruance, who always kept the ultimate mission in mind. Spruance had to keep Mitcher on a tight leash (even then he would jump the gun, as he did with the Yamato, launching well before Spruance had decided to use airpower to kill her rather than one lest big gun showdown) while Mitcher had to run to keep up with Halsey.
Both men had great success (it is an open question if Spruance would have sent Washington and South Dakota, with only four destroyers, into the Slot in November of 1942 which turned out to be one of the best tactical decisions of the War), but they were very different.
I want to reply about if Spruance would have sent those ships to the slot in November 1942. Yes he would because the Enterprise was the only carrier avaible and damage at the time and he would have to take that risk if Guadacanal wants to survive.