Hedging Case Scenario`

Hey guys, let's consider a hypothetical scenario. First up, we all know we got various options to hedge our position some of them being spx or spy etc. Now spx is quite a large index as its 10x of spy so if u are holding a 10M or 20M portfolio, and u want to hedge out positions which index would u prefer?? Will it be a cash settled index spx as u r already holding shares and can't afford exercise risk or will it be spy. Anyone hedging there portfolio, size should not be the barrier. So do institutions mostly prefer spx or spy for sole purpose of hedging??