When transitioning to the civilian sector. What career field most closely resembles the military way of life?

I'm Infantry, so the civilian job that most closely resembles that would be Rock Star.

After dealing with some of the shenanigans of young Marines and the enthusiasm of 2nd Lts I think I could have been a professional Goat Herder.
Seriuosly, it probably depends on the MOS you held.

Defense contracting is the closest in terms of doing the same job that you may have had in the military. Instead of a commander you have a program manager or site lead. Than you have line supervisors. Sometimes the lines are blurred on who owns you. You may work for a company you are the sub of a contract where your manager for that company is out of state. Your actual day to day boss is actually employed by another company.

The pros are being able to slide into a job you already were trained at doing the same tasks.

The cons are that you are no longer in the military and work solely for the government. You are no longer in the military so you work FOR your peers and in some cases previous subordinates So what ever your previous rank was or is (for reservists) does not matter. The focus is no longer mission accomplishment more than it is contractual compliance. Making sure you meet all the tasks in the performance work statement is sight line for the contractor.

Contractors do not get as much time off as military so 30 days of paid leave is out the window. Many companies it is two or three weeks. all your time must be accounted for. It can be a challenging environment when you leave. Your expectations are that it is going to be the same as the military but it isn't always. The good news is that you can find a job fits you if the first one doesn't. It is not uncommon for contractors to bounce around.