Should I transfer to another MOS to help me get job outside the military or should I apply to a government job using my current MOS?

I find it weird when people ask what job they should do for a career outside the military, when they have an actual career with Healthcare, 401K, guaranteed pay raises, 30 days of vacation time a year and a guaranteed pension after 20 years.

I mean, if you hate the military then get out and do something you like. But if you like what you're doing you'll be hard pressed to find a job where you can stop working after 20 years and keep getting paid, that has so many free benefits and no union dues or health care costs

35S can lead you into working for an employer that usually goes by 3 letters.

Nobody can tell you want you want but you. You could stick with the current MOS, lat move to another job field , get out or you could go the NG/ reserves route if you want to have one foot in each world. These are all viable options and without knowing you I have no idea what to recommend.