Conte won the Premier League in his first season at Chelsea whereas Mourinho has suffered a frustrating campaign at Manchester United.
The Red Devils have won the EFL Cup and can qualify for the Champions League if they beat Ajax in the Europa League final tomorrow but they ended a disappointing sixth in the league table.
Mourinho has cut an angry figure in recent months at Old Trafford due to the amount of games his side have had to play towards the end of the season.
BBC Radio 5 Live pundit Pat Nevin remembered how the Portuguese was happy when he returned to Chelsea a couple of years ago.
"I remember he came back and he said he was the happy one just over two years ago," he said.
Premier League 2015/16 wages compared to 2014/15 Sat, May 20, 2017
Express Sport brings you a comparison of Premier League wages from the 2014/15 and 2015/16 seasons
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Arsenal – 2015/16: £195.4m, 2014/15: £192.3m
Chris Sutton has suggested Manchester United's Jose Mourinho is jealous of Chelsea's Antonio Conte
Is Jose Mourinho jealous of Antonio Conte?
Chris Sutton on Manchester United boss Jose Mourinho
Sutton then put the question "Is he jealous of Conte?" to Nevin, who thinks he doesn't care about anyone else.
"I think he's so one dimensional he wouldn't care about anyone else unless he's winning," Nevin responded.
"He couldn't care less if he's winning."
Former Manchester City defender Danny Mills says that's why Mourinho hasn't been happy, because United haven't been winning.
He said: "That's what it comes down to. He's not winning.
"Every other club that he's been at, he's been a winner."
Pat Nevin was disappointed Jose Mourinho refused to talk after Manchester United's last game
Mourinho refused to talk to the press after the 2-0 win over Crystal Palace on Sunday and Nevin was disappointed he didn't come out and talk about the youngsters who impressed in the game at Old Trafford.
"Somebody said yesterday on the radio that the fact Jose didn't come out and even talk to the press about the kids and I couldn't believe it," he said.
"That's a very good point. Of all the points of him not talking to the press, you know he's not getting any respect from the press and it's just a game anyway but you know what, some of those kids came in and had that moment, that would have been nice to go and celebrate that.
"That was a big disappointment."