Becoming an RN is going to take a lot longer (probably 4+ years longer) if you enlist first, just given the logistics and requirements of those enlisted to officer programs.
I can't speak from anything other than a nursing perspective. Nursing in any of the 3 branches is fairly similar, based on my interactions with Navy and Army nurses. The differences are in things like culture and tradition, but that doesn't impact your day to day job a ton in my opinion.
The Air Force Nurse Corps really believes in specialization. They are really strict about requirements for attaining specialty codes, such as those for ICU, ER, or OR. The Air Force likes formal courses. They will require a med-surg nurse to attend a 1 year training program to do ER or ICU for example. This tends to lock you into a specialty for many years and is nice for people who know what they want to do.
From what I have seen of the Navy, they value jacks-of-all-trades. They have specialty codes for ICU, ER, etc, but they often train on the job. They don't send you to a formal training program at a faraway base. Since they are easier to get, Navy nurses seem to acquire more specialty codes over their careers. It might suit people who want to do a little bit of everything.
Most nurses in the military work in a hospital on land, but there are special jobs that differ by branch. In general, the vast majority of flight nursing and air evac is done by the Air Force. All branches have some air evac teams, but the Air Force does almost all of it for all 3 branches. The Navy offers some great ship nursing opportunities, and they have 2 hospital ships that just do humanitarian missions. The Army offers nurses the ability to embed with tactical units (brigade nurse). All 3 branches have some form of a small, mobile, surgical team that deploys to remote areas; the AF has special operations surgical team (SOST) for example.