Factually speaking, Jose Mourinho isn't a better manager than LVG if we take into account the holistic aspects of football.
In terms of trophies won, LVG had 18 seasons in football Club management, won 7 titles, several domestic cup titles, reached champions league finals thrice, won 1 of them, one of the two losses were in penalties. Jose is managing his 15th season in Club management, won 1 more title (probably will never win another unless he manages somewhere like League One), but reached champions league final once less than LVG, but won both champions leagues by thoroughly playing Helenio Herrera type of super negative football, very much unlike that of Ajax in 95.
In terms of long term legacy in football, LVG trumps above Jose by miles. LVG promoted youth everywhere he was, whether that is forced by injuries or whether those players were too talented to be ignored or whether those players were discovered by others, it's a fact that, LVG promoted youth that kept serving all the clubs years after he had been fired. Yes, he may not be a genuine football *********** like Johan Cruyff and he did not revolutionize Barcelona, but he maintained the continuity of the dutch style at Barcelona when Cruff left in 90s, LVG's role was, in that sense, crucial to Barcelona's evolution despite his failure in 2003.
Jose has never kept such legacy anywhere at any club he has been to. His managerial style in very short term only prioritizing the present moment.
In terms of failure, LVG had the worst failure at Barca in 2003, which is pretty much matched by Jose's failure at Chelsea last year. Apart from Uniao De Leiria, Porto and Inter Jose has been sacked everywhere, LVG too has been sacked everywhere except Ajax and AZ. Yes, LVG may have failed with the dutch once, but he more than made up for it in WC2014.
So, overall, LVG did not have any worse career than Jose, he is or was no worse manager than Jose. One thing is for sure proven now, both the managers are things of past (Yes, already 11pts behind after just 13 matches proves Jose cannot succeed at United). Football management is past them, both should hang retire now, LVG already seemed to have, I'd be glad to see the back of Jose too.
In conclusion, LVG should have been replaced by someone like Klopp, Pep Guardiola or Mauricio Pochettino, they would have never taken a U-turn from all the work LVG has done and set us back to square one, the place where Moyes left us. Mourinho is the last man in the universe, not just on earth, we should have appointed as the manager. He is only successful when the team is ready, not for a rebuilding or revival task, he has never done any revival at any club, he has only managed clubs who were on the rise, not who were on the fall.