Actually Mancini and Pellegrini won titles already with weaker squads. Plus they also won some other domestic trophies...
Pep have more in quantity but he got lucky many times to win CS, Fa cup, League Cup on penalties.
In the end of the day PL and CL are what matters the most.
If Pep fails to win CL this season that would mean 2 PL and 0 CL in four years. With this squad I am sure they wanted more. He did not even reach semi final yet unlike Pellegrini.
And every season he got knocked out by weaker squad: young Monaco team, Liverpool 17-18 and Spurs... They also spent more money than any other team in the world in this period.