Both public and private blockchains run the risk of being mutated, i.e. retroactively changed. They just use a different security model for preventing a minority of participants from doing this.
To mutate a public blockchain based on proof of work, there needs to be malicious collusion between the parties who collectively own 51% of the mining capacity of that chain.
To mutate a private blockchain based on round-robin distributed consensus with a mining diversity 0 ≤ d ≤ 1 and m > 0 permitted miners, there needs to be malicious collusion between at least m × d of those permitted miners.
These two risks can't really be quantitatively compared, because they are different types of risk.
Libertarians can live with the 51% proof of work risk, but not the round-robin one, because they don't want to be dependent on any kind of centralized or authoritarian structure.
Enterprises who have signed contracts regarding a blockchain they use collectively can live with the round-robin one, but not with being dependent on anonymous proof-of-work mining, because they have the court system as recourse.
