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.
The owners of Chelsea are not having any patience, they want results because they have spend too much money on the club but they are not seeing their money being used very well to better Chelsea as a football club. Pochettino would not have taken Chelsea to the level the owners of Chelsea want to see Chelsea playing at. There is no time to give the coach that chance to build up the team slowly, they want a fast response and for Chelsea to be playing with the top clubs. The sacking of pochettino is not going to be a regret by the board because he is not the right man for the job in spite of how well Chelsea were playing at the end of the season but by then it was already late because he did not start strong when the fans and everybody were expecting him to use his experience to make the players play good football.