There are people better qualified than me to reply; Prestwich blue being your man.
Niether Club has challenged it. However City supporters club and PSG supporter club are part of DuPont's case against UEFA as affected consumers. Part of the argument as consumers is, as I understand it, that the clubs will have to increase ticket prices in order to increase revenue, to stay competitive. This is because by UEFA's ffp model they have placed restrictions on how much an owner can invest into their business. This means revenues have to be raised primarily by sponsorship deals, match day income, tv deals, competions and merchandise. As City and PSG have not had a long history of sustained success neither club can command as high a sponsorship deal as the established clubs. All of whom gained their position initially by owner investment far surpassing what their revenue streams were at the time. As owners are limited to what they can invest then the argument is it will inevitably lead to an increase burden on the fans (match going ones) to pick up the slack. It will also entrench the position of the so called 'big clubs' protecting their advantageous position - stiffling true competition.
In reality this is a far bigger problem to PSG than City as their league has less TV money and global appeal. Also French tax laws mean they are at a disadvantage and have to pay higher salaries to compensate for the higher tax paid in France. City are in a better position due to the premier league money and also because City are one club in a football group. City's idea with the City football group is obviously to attract sponsors by offering exposure on many continents and therefore increase revenues for the whole group. Most City fans i know arr against it as we see it as immoral. We know we won the lottery when the sheik bought the club, but are not against other clubs being lucky as well. Think it is good to have a truely competitive league. Unlike arsenal, rags etc I don't think our owners are scared of healthy competion.
City made it very clear they were extremely angry about the rule changes that were brought in AFTER our books had been submitted for ffp inspection that led to us 'failing' ffp. Think it is pretty clear they left UEFA in no doubt that there would be court action if it was tried again. Personally I think City or PSG would win any court action because it has to be anti competitive. Our club has no debt, the sheik has put it all in equity. Therefore there is no risk to the club, with the hypothetical scenario of the sheik asking for his money back, which would be the case if the money was loaned to the club like other owners have done, abromovich being one. The club and its revenues have grown hugely so it is difficult to say the sheiks business model isn't working. His personal wealth is so great that his investment in City is small in comparison and if he wanted to continue investing at the rate he did in 2010, placing it in to equity he clearly could. However that clearly never was his plan to behave as a 'sugar daddy' it was projected large scale investment to eventually make profit's and have fun on the way. He is following a business plan. Can't see how a court would see it any other way and UEFA's efforts to prevent him from investing in his own business at no risk to the club would be slaughtered. As footballers are professionals and have a career can't see how it could be argued football is purely a sport, and outside of normal business laws particularly when it has billions of pounds swilling around. So being blocked from UEFA competions, when you have satisfied the qualification process to compete because you have fallen foul of cartel protectionism wouldn't wash I think. Saying it is an invitation competion would be shown up as the champions league has no precedent to say that is the case (to my knowledge). Participating is the only way you gain sponsorship thus improving your business.
City didn't challenge it for 2 reasons I think. 1. It would take years and end up being a pyrrhic victory. By the time its won you would be so far off the pace, and no top players would have joined the club. 2. Financially City were/are in a strong and improving situation where the fine and punishments were 'a pinch' in the long term trajectory of the club. Ffp is being slackened for new owners simply because it is clear that it will now have a limited impact on the club
Sorry for the long post,