This is only a superficial difference. On a relatively big economy like France, the difference between state-based pension and capital-based ones are very minor

This is only a superficial difference. On a relatively big economy like France, the difference between state-based pension and capital-based ones are very minor: in both cases, you're hoping that people who work when you retire will be able to pay for your retirement. Private funds in UK are severely underfunded by the way (although I can't find a reference on the exact number, which is supposed to be around 250 billions pounds), in the same that state-based systems are underfunded. The main factor for retirement is the 'working people'/retired people ratio (ration de dependence in French, not sure about the proper English translation), much more than how it is funded. Governments can easily change tax benefits/incentives on those funds, so the taxation aspect is not that different either.