Potter was given the reins of the Chelsea team last week after the club decided to sack their Champions League and Club World Cup winning manager Thomas Tuchel following a slow start to the season.
Ten Hag took charge of Manchester United at the end of last season and following a bad start, the Dutchman has stabilised things at Old Trafford with four league wins on the trot.
There are already parallels being drawn between Potter and Ten Hag, who are both in charge of big clubs, but Melchiot stressed that his fellow Dutchman has the harder job and is under more pressure.
He pointed out that Potter is at the start of a journey with new Chelsea owners who brought him in to replace the manager from the old regime.
However, he feels Ten Hag has the bigger job due to the circumstances at Manchester United and stressed that he has been dealing with the pressure even before he became their manager.
Asked who is under more pressure and has the bigger job between Ten Hag and Potter, the former defender told ESPN FC: “By far, Ten Hag has got a way harder job than Potter.
“Potter comes in and the way he came in is that he got brought in by the new owners.
“They wanted to have a clean and new slate and he is part of the journey.
“He doesn’t come in with pressure but Ten Hag, even before he got the job, he already had the pressure with signing the deal.”
Potter will take charge of his Chelsea team for the first time when they will take on RB Salzburg in the Champions League on Wednesday night.