Apply for any job that you may find interesting. Once you get an offer, do the analysis to see what you are looking at regarding pay cut, COL, job security, potential promotions, pensions, retirement fund matching etc.
My husband is a civilian and the benefits definitely need to be taken into account when doing the analysis. I stayed a contractor to go for the big bucks but that's a bit more risky as far as no defined pension, more employer changes, etc. We decided for him to work as a govt employee to offset the risk of my job. One of us would always be pulling in a paycheck but you are right, public sector pays less.