As an army medic you will be a 91W MOS. The army recently transitioned all medics from 91B to 91W. Basically, the MOS change requires are medics to become EMT-B certified. You will come into the army as a 91W since you are brand new. You will go to Ft. Sam Houston in San Antonio for Basic and AIT. In AIT you will go through the EMT-Basic course, Trauma AIMS, and BTLS. These three courses are the heart of your knowledge as a medic. You are essentially at an EMT-I level.
After graduation from AIT, you will be assigned to any one of the glamorous army posts throughout the world. You could end up working in a hospital, a clinic, or even in a line-unit. If you really want to get out and use your skills, you want to get down to a combat arms unit (infantry, armor, artillery). There, you will most likely serve as a platoon medic...probably the job you imagine when you think about being an army medic. You will be "the doc" for a 20-40 man unit. You will work under the supervision of the battalion PA or MD, but when you go to the field, you are the man. There's no one looking over your shoulder. It's just you. In this regard, the army alows you a much broader scope of practice than the civilian world. You will be authorized to give IVs and meds as well as perform trauma procedures such a needle decompressions and advanced airway maneuvers. I see this as an advantage, but it certainly can have its disadvantages as well. Additionally, the leadership of the platoon will rely on you to train the soldiers in basic medical skills combat lifesaver) as you are the subject matter expert. Being an infantryman, this is the side of the medics that I know best. I can't tell you much about the hospital side of the house, but know it does exist. Personally, I think you might see more stuff because you're working around specialists and docs, but your level of responsibility is much lower...ie taking patient information, taking bp, getting supplies.
Yes, there are probably more PAs in the military, but like medics, PAs are allowed much more freedom than the civilian world. Alot of these guys are former medics or 18Ds. There is plenty of experience there and you certainly would not be at a disadvantage working with them. In fact, in the trauma world, ie combat environment, alot of these guys will have more knowledge than the FPs that get attached to units for deployments.
If you're really gung-ho, consider the 18D route, which is a Special Forces medic. It's a whole different world. Training is very intense but their scope of practive is amazing.
Hope that helps.