Pros
The primary reason why the Academy continues as it does is the $. Both military and civilian are paid far too much for what they do. So the pro, if you are an employee, is the income. The benefits are not bad, of course, and people are generally respectful, to your face anyway.
Cons
As a civilian academic, the cons are considerable: working for a US military employer, it is the ranks of the US military that run the show, make all of the key decisions (despite lip service to the contrary). The culture is largely 'be at your workstation' and fill-out - seriously, for all employees including professors - time cards. Yes, time cards. Most importantly, the US Coast Guard Academy, unlike other US military academies, forces all cadets to take trainings that seriously impede their ability to pursue an education. The cadets are perpetually in survival mode, putting out fires, and not doing any serious study of any kind, on any topic.