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 don't know, I do not think that firing Pochettino was a big mistake, I feel like he did not do all that well with the team he was given. I get that they are getting young players for overpriced offers so that they could build a team that would play together for a long time, and that could actually be a great idea on the long run, and they are avoiding the financial fair play hit by just giving them very long contracts as well.
However, unless they make something now, like at least be in UCL or something, then they are not going to get anything at all, being a loser for a few years doesn't make you great, you need to have good results, to aim for great results, you do not get bad results to aim for greater results.