While I have only done AF nursing, I've interacted with Army and Navy nurses and have some idea.
If you want to do flight nursing or some form of critical care air evac, then the AF is what you should do. Yes, the other branches have flight nursing, but the opportunities are far more limited. The Navy has some really good bases (San Diego, DC) , since they tend to be by the coast. The Navy also has ship postings, such as a ship's nurse on an Aircraft carrier.
The Navy doesn't like ADN/diploma nursing. If some of your RN experience was earned without a BSN, the Navy won't give you credit.
The Navy embraces the 'jack-of-all-trades' mentality a bit more than the AF does. Both branches have specialty codes, but Navy nurses tend to acquire more of them more easily. The AF loves specialization and feels more corporate. If you want to try a bit of everything, then the Navy is your show. The AF allows you to do one thing for a long time (ICU, ER, OR, L&D, NICU, and psych especially so).
Honestly, though the overall career/job is very similar. At many bases Navy and AF nurses work side by side on the same unit.