The Sunday Supplement line-up of Holt, Steve Bates and Matt Dickinson debated the power struggle and mind games between the two managers ahead of the mouth-watering Monday Night Football clash between Manchester United and Chelsea.
The trio have been impressed with how Moyes has begun the daunting task of succeeding Sir Alex Ferguson at Old Trafford. In particular they approved of how United have fended off Chelsea's advances towards Wayne Rooney and prevented their rivals' open pursuit of one of their star players from destabilising the squad.
And as well as a cracking contest on the pitch, the journos are expecting a potentially explosive confrontation on the touchline with Moyes, they say, certain to match Mourinho's fire.
"We saw Mourinho's new mask of ambassadorial dignity slip in midweek against Aston Villa," Holt told Sunday Supplement, in regards to Mourinho's criticism of Villa boss Paul Lambert following Chelsea's victory in midweek.
"I think when Mourinho got the job and it also became evident that Sir Alex Ferguson was not going to be at Manchester United - it was going to be David Moyes - a lot of people felt that Mourinho would target Moyes psychologically and just test him out.
"I think he has done that. I think the Rooney transfer saga has been his perfect way of doing that. To be fair to Moyes and (Ed) Woodward at Manchester United, they have stood up to that and they haven't blinked. They have stayed firm about the fact that Rooney will not be sold.
"There is still a little while to go but it is looking that Rooney won't go, he certainly won't go to Chelsea they say. So I think Moyes has stood up to it ok so far. He is used to this kind of thing and he is hard enough.
"If you are talking about confrontation remember how he (Moyes) stood up to Fergie. Moyes is not afraid of going toe-to-toe in a screaming match with Alex Ferguson so he will not be shy about taking on Jose Mourinho."
The Times' Dickinson believes Mourinho is relishing the opportunity to present himself as the elder statesman, or 'Godfather of the Premier League', following the retirement of Ferguson, and as he contends with Maneul Pellegrini at Manchester City and Moyes at United.
"That (The Godfather) is certainly how he is portraying himself, especially with Pellegrini new, with Moyes taking the big step up to United. It is as if from the start Mourinho is trying to set himself up, as you say, the Godfather of the Premier League - the guy with the know-how, the experience and the clout.
"It is a role he is relishing and he has a team that is right up there competing. It is a fascinating game because both managers are still feeling their way with their teams as well."
Bates, from the Sunday People, insists Moyes is filling the void of Ferguson at Old Trafford with remarkable ease so far, which he thinks makes Monday night's showdown all the more fascinating.
"I think he is growing into the job very well indeed," he said. "I have been to a couple of his press conferences. At his one on Friday he was very much at ease in dealing with the topics you have to deal with.
"I certainly see him relishing coming up against Mourinho. I know it is early in the season but it is a good early test for him and for the team. From what we saw at Swansea they have shown that they have still got the class and ability to back up the manager. I can see it being a fascinating contest on Monday."