What military group has the best medics?

There are only two services that have "medics," the US Army and US Air Force. Medical personnel of this type in the Navy are referred to as Corpsmen. There are no medic MOS's in the US Marines.

Of all combat medical personnel of enlisted ranks, US Army Ranger medics, and those who serve as US Navy SEALs and USAF Para Rescue are perhaps the most comprehensively trained. Although, all Medics and Corpsmen are heroes in their own right.