It might come from other factors than aging. The incentives are different and the way the structure evolve too. In public institutions, political tempo affects operations.. every new head of minister will reorganize things for a short while and then issues start showing up, until the next election. It makes people unable to care for efficiency after a while because they know how often friction will grow again.

Maybe small difference in finances too, very often public sector struggles with basic tools. I "feel" that private sector is a little more prone to renew that part (to satisfy the efficiency gods). That said it often backfires because they will also replace perfectly good tools or software to get the latest shiny.

Then there's mass.. but large private corps will have the same issues.