I'm not sure I can do much on the U.S.
In terms of Great Britain, our histories have diverged. They have a person called the Judge Advocate General, as do we, but he fills a very different role in the United Kingdom than our JAG does. Our JAG is, among other things, the adviser to the government on issues relating to military justice. The JAG in Great Britain does more than this, but largely his role is to appoint military judges. It's a very different role.
As with so many things in the United Kingdom, their system of military justice is being challenged by the process of Europeanization. It's a live question whether Great Britain is going to remain in the EU because of the pressures they feel, the potential incompatibility between the common law way of doing things and the continental way of doing things, as is embodied in the EU.
That's a brief answer.