I think personally it would be the other way round, Pochettino will be more successful compared to Ten Hag if he managed United because they really fell out by ending below Chelsea.
Every coach will certainly be great if he has a productive main squad, it doesn't matter if it's Pochettino or Tenhag if it is not supported by a productive main squad of players it will also be useless, we can indeed see that Chelsea is much better than Manchester United in the EPL this season but success It's not entirely because of the coach, if Pochettino replaces Ten Hag without financial support it will be useless because Manchester United needs to make a lot of changes because many of their players are really unproductive.
I think we all know that Pochettino being fired by Chelsea was a big mistake, that's why it will be difficult for Chelsea to achieve satisfactory results if management is too quick to make the decision to fire the coach, I don't think Pochettino is too bad for Chelsea because he has brought Chelsea to a high ranking. well in the EPL this season, if only Chelsea gave him the opportunity to stay until next season the results would definitely be satisfactory, Chelsea seems to be working hard again with their new coach and Manchester United has not yet made a decision about whether Ten Hag will be fired or retained.
Yes, the quality of squad available to the coach plays an important role on the outcome of the team in various leagues, if the team are quality enough probably at their own best they might achieve better results than a club with a better coach and less potential players. If peradventure the both managers are to swap teams then Pochettino will do better managing United than Ten Hag on Chelsea, it's my own observation without being biased I always feel this connection between Pochettino and his players. Chelsea really made an awful decision letting him go so easy, he would have done better in more season to come. Manchester United are keeping Ten Hag for another season, let's see how he does this time.
I think Ten Hag lasted longer at Manchester United. I would also like Pochettino to be the person to manage a team full of success like Manchester United, because Ten Hag does not know the opportunities he has. He can't use it correctly. I think they should be dismissed from that team and move on with a better candidate. I don't understand why Manchester United management is giving him a chance because he can't manage as well as Arteta. Arteta is doing everything for Arsenal and it is understandable that he did not provide continuity, but I think Ten Hag is managing terribly.
Ten Hag is not going anywhere at least for 1st 10-15 matches of EPL and he is doing well yes he cannot get the best from some of the players but he did good for the team and ManU management is happy with him after Man U beat Man city in final and won the cup.
maybe I'm wrong in my way of seeing things, in my way of seeing, a team like Manchester United that has the money to be able to sign the best players in the world, should be candidates for the title every season and should be a team They would have gone far in the European Champions League, but what we see today from Manchester United is a disgrace. Even teams with less funds than Manchester United can do better in the Premier League, an example of what I'm talking about is the case of Aston Villa who finished in the top 4

Aston Villa proved that when a team has a good coach, even with limited resources, it can achieve great things, and they managed to finish in a position to access the European Champions League, while a team like Manchester United, which has great financial resources, was unable to do so. finishing in the top 4, it is clear that the Manchester United coach is not good enough, but for some strange reason it seems that the Manchester United management does not see this. my question:
What is the goal of Manchester United?
Aston Villa agree on deal with Luton Town to sign Ross Barkley
Fee now agreed between clubs, in the region of £5m.
Final part needed, medical and signature with player's side agreement now expected at the beginning of July.
Unai Emery wanted Barkley as experienced and quality player to improve the midfield ahead of UCL season.

source: https://www.instagram.com/p/C7wRN-jIo89/After Aston Villa had an excellent campaign last season, the Aston Villa coach continues to improve the squad even further, probably so that it can continue with a good campaign next season in the Premier League and be able to go far in the European Champions League.