First we should establish an apples-to-apples comparison, and the best way to do this is by comparing the annual package, including
CPF contribution. Why do I say this? Because in many cases nowadays, Private Sector pays higher basic pay, and few months' bonus. Some do not even offer 13th month. On the other hand public sector typically has low base pay, but typically gives 4 months' of PB and AWS bonuses.
In cases were Private Sector pays 13-14 months whereas Public Sector is 16-17 months, the difference is not just in take-home pay, but also Employer
CPF contributions, which average about $1K a month. Plus, Public Sector gives 2% additional Medisave contribution (not a good trade-off if you are older, but good if you are young and single).
Based on my calculations, if one was previously on a 14-month private sector package and switches to a 16-month public sector package, he/she can afford to take about 15% take-home pay cut while still maintaining largely similar annual package.
Then, if on top of this one is willing to forego 10-15% in annual pay for Public Sector's greater job stability, then a take-home pay cut of 25-30% is very likely.