Well, United presumably had a better team than Everton after Ferguson left but it didn't stop Moyes finishing below them.
Both Ole and Ten Hag have finished above Klopp's Liverpool recently, and I assume Carragher wouldn't say United had a better side than Liverpool in that time period.
League position isn't just determined by first 11, but by the entire squad. And it's also determined by mood and motivation within the squad and how the players feel about the manager. We've seen through history that when the long term popular manager leaves it can cause a downturn in results when the new manager comes in.
Neville has some weird opinions, but I don't think predicting Liverpool dropping off after Klopp left is particularly weird. He's probably hoping it happens as much as he's predicting it, but it's also got a fair chance of being true.
Having said that, I have no faith in United and we're still probably 3 signings away from being confident in the side. City/Arsenal will be top 2 but I think the others all have the potential to be anywhere from 3rd-8th. Liverpool are favourites for 3rd in my book but it wouldn't be a shock if they finished outside top 4.