You can write a multiple page essay about this, but here rightfully nobody cares, so let's say it short, normally you shouldn't need to compare these two guys, Mintzlaff was good as the CEO and looking over the financial stuff, also he's very good with Mateschitz.
But since 2019 he has made himself something like an absolutist monarch after Rangnick left with the hiring of Krosche (normally the guy only was supposed to be an assistant for Rangnick and look at the cooperation with Paderborn which was torn down by their fans, suddenly he was the main sporting director and Rangnick gone), who he fired this year because his signings were total shit (like letting Schick go for being too expensive but then buying useless Sorloth for nearly the same and burning a ton of money in other transfers). Now he hasn't hired any new guy and is basically the boss for everything while having absolutely zero background in football so having no knowledge of what you need. So yes, Red Bull football before Rangnick was a waste of money and completely shit and now it looks like it will go that road again. Salzburg is still in good hands thanks to the scouting network he built and their sporting director Christoph Freund is a direct student of Rangnick so he makes the same good transfers (but he's a Leipzig hater so that doesn't help the entire system).
The team is built for Nagelsmann at this point so when you look at what was said today, the team didn't want to go back to pure pressing (rightfully so) and stay with the Nagelsmann possession system which Marsch while somewhat trying had no idea to teach (here another Mintzlaff masterclass comes to play selling all of Nagelsmann's assistants for change even though Nagelsmann said initially he won't take them with him).
This is the main worry I'd have as United, what he'll do when teams start parking the bus. This is always the issue with the Red Bull pressing teams. In 18/19 after a very bad start he found a solid way being monsters at set pieces and for a Rangnick team very good with the ball. If he just goes hiring Ten Hag in the summer while buying the right players it could turn out to be a non-issue anyway and after hiring Nagelsmann I very well could see him do it again. You can look at the guys he bought for Bragantino as well, they are in the 2nd season in the 1st tier and just were in the South American Europa final and could qualify for Libertadores now. His team building with Ten Hag as coach could be a juggernaut quickly.