Comments by Mosley on Sunday might be interpreted as the battle's opening salvo, when he said Todt was partly to blame for the financial struggle of many F1 teams because he "was never a friend of cost limits".
"Now formula one has a big problem," Mosley told Welt am Sonntag newspaper.
Also asked about F1's financial crisis, and the fact many fans are bemoaning the confusing state of the sport at present, former driver and team owner Gerhard Berger also pointed a finger.
Asked specifically if the sport needs a shakeup, the Austrian told Bild am Sonntag: "The time is probably ripe.
"In formula one, the old adage 'too many cooks spoil the broth' is more and more true.
"Previously, Max Mosley and Bernie Ecclestone worked as a unit. But today we have in Jean Todt and Ecclestone two chefs who have different tastes and different spices.
"This leads us to something that is expensive and also difficult for many of the fans to understand."
A big problem, Berger added, is the constantly-changing rules, overseen and governed by the Todt-led FIA.
"In football, you could also make the field bigger, smaller, allow 15 players, 10 players, make the goal bigger, smaller. But they don't.
"Football is easy to understand, but this is a difficult moment in formula one."
Not only that, Berger said constantly-changing rules are associated with "insane costs" for the middle-ranked teams, in a market of declining sponsorship.
Like many purists, he is particularly critical of recent developments such as DRS, the moveable rear wing flap that has all but replaced the more traditional - although rare - species of overtaking.
"I don't like these ways to artificially improve the show," Berger admitted. "And I honestly believe that it's the same for the fans as well. They want a real sport."
And, like Mosley, Berger gives a vote of confidence to Ecclestone, even though the 82-year-old Briton is facing bribery charges that could bring him down.
"He has led this sport for decades with perfection, vision, cunning and hard work to great success, for which we all have to thank him," said Berger.
"As long as he is fit, there is no one better.
"But formula one is owned by the investment group CVC, who would normally hang on to an investment for up to ten years. And that time is basically up.
"I believe that a reorganisation is necessary and quite possible," he said, "and the FIA and Todt will play an important role."