Given the we'll say "limited" nature of the game probably House. If this were a real life scenario where interactions are more meaningful and relationships actually exist, I'd argue independent Vegas. The courier themselves are just a merc with mail, basically independence incarnate. If we assume they're an average person just with an 18 karat run of bad luck AND they did go after the chip instead of disappering they would probably have negative opinions of everyone.
Caesar is an egomaniacal tyrant.
Kimball is a useful idiot whose administration breeds corruption.
House is an egomaniacal, tyrannical asshole who'd do anything to stay on top and is far too reliant on tech.
Traveling the wastes, hearing stories and definitely seeing the state of Vegas and the Strip would be the foundation of 6's opinions. In every scenario of the big 3, the wasteland would continue to fight regardless of who's in charge and more death and destruction would follow win or lose.
So if we're being realistic, I would think 6 would probably (including DLC) kill Elijah, blow up Big MT, fight the White Legs and spare the leader, kill Ulysses to stop the nukes, kill House, kill Caesar, stop Kimball's assassination and install Yes Man. They'd probably help the NCR with most tasks incidentally making them respected especially by conscripts and the most grizzled vets. When Hoover dam happens, Oliver would be forcibly removed and a large portion of troops would stand down both at the dam and across the Mojave either deserting or returning home. Once the dust settles they'd clean up the families, take Yes Man offline so there's 0 central leadership then disappear.
If every major scenario ends in continued conflict, oppression, destruction and death, the logical answer would be control it as much as possible and eliminate all major players to decentralize power. Let everyone else decide.
Ultimately in the end there's no winning. Freedom is the only principle worth fighting for regardless of the road travelled to get there. Even if the factions could maintain oppressive control, they would eventually collapse and lose control of Vegas. Caesar and House will die, they hold their factions together, and the NCR will shed Vegas the first chance it gets as it requires too many resources and they're already spread thin.
Cut the filler skip to the end result.