I was never in the military, so I don't know if the average care is better than that or not...but my guess is it isn't.
When I was in basic training I had the misfortune of contracting advanced conjuctivitis. In lay terms, it's pink eye on steroids. I was hospitalized for about a week. Pus filled blurry eyes, intense ear aches, sinus and throat pain, you name it. I was pretty much blind with the disease. During my stay there they tried everything under the sun, from anti-inflammitories, to anti-allergens, when it was clearly an infection. Finally I managed to get a different doctor to prescribe me some powerful antibiotics (After about three days.) I started improving within a day.
Now I, not being a doctor or having any training in medicine, was pretty damn sure it was an infection from day 1, but would they listen to me? Not until everything they thought would work, didn't.
So yeah, free health care blows no matter who you get it from. The only positive aspect of it is the free part.