Hi, its good that you already have a understanding of what you want to do. I myself don't know much, to nothing about the nursing course provided in both army and RAF. However i can almost certainly guarantee that you will travel in both of the forces. Me not being biased (having already applied for the RAF) would go for the RAF due to the more likely chance of you being a flight nurse.
Like i said i myself am not even fully into the RAF yet but hoping that this can give you a bit of understanding. You could also find out probably a lot more if you dug a bit deeper into the internet about people who are already doing the job you want.