Would you feel safer being in the Military during a World war...?

During a hypothetical World War III?

Military, no question. The military will receive "reasonable" supplies of food, medicine, and protection, if they aren't vaporized in a nuclear blast during the first few hours of the nuclear phase of the war. This is because the military will be essential to keep order, and they will need to be kept loyal and effective - or as loyal and effective as would be possible.

A citizen in a major city will almost certainly die - either instantly, or slowly of injuries or radiation poisoning.

As was written about "the Constable" in the alternate history story "Protect and Survive," which is a highly detailed and plausible look at the aftermath in Britain of a nuclear war in 1983, "choose the $@%@# cowboys." The Constable did horrible things during the aftermath of the war - he summarily executed civilians, worked as a guard in what amounted to slave labor gangs - but he survived because he was part of the authority.

I'm very safe on the left coast far from any major cities.