Have you factored in the bonus structure between the two companies? Ministry is offering AWS + 3-4 months bonus and your current company offering? I am not sure if the pay cut you mentioned is just on the basic and I believe they will consider the annual package before giving your the offer.

If based on 3.5 months variable bonus and AWS 1 month, the annual package they are offing is $77,550 which is reasonable for 3 years experience unless you are getting above that amount now.

What is your reason to switch to Civil sector now? You may have to ask yourself about the job prospect of your current job before considering the difference in remuneration package.