It’s very difficult to say with any authority.
A private pension depends on how much you contribute along the way whereas a public sector pension, as outlined above, is now conditional on the salaries of the grades you’ve occupied and the length of time you spent in each grade.
Whilst you previously would have been guaranteed a pension 50% of your final salary (assuming 40 years service) at age 60, anyone entering since 2013 can anticipate a much lower percentage and will have to wait until 65 at the earliest. The percentage they get won’t really be known until they retire as it depends on how quickly they’ve progressed in previous years.
A proper comparison would require information on income, proportion of income apportioned to pension, age, anticipated age of retirement etc.