With Hawaii now Joint Base and many other installations doing the same (Joint Region in Guam) with Air Force seemingly pairing up with Navy or Army installations (I think Alaska is Army and Air Force joint base now), it will be interesting to see what will happen on the Air Force section of the installation. Or what was formerly the Air Force section, like Hickam here.
Bases have a "host" branch, and a Base Commander, The Base Commander is separate from the tenant commands. He deals with facilities, housing, roads, hospitals and infirmaries, gyms, AAFES, NEX, gas stations and other concessions, rec centers, and on and on.
The Base Commander is also responsible for base security. If he decides to pass a base reg that allows concealed carry, it will apply to all tenant organization regardless of branch.
Having said that, a tenant command could then initiate a local reg prohibiting carry for anyone in their unit. Therefore, in cases of joint bases, the Air Force host commander, for example, could allow CCW, for all personnel which the Air Force units are good with, but the Navy units on base could prohibit it for Navy members and families.
I've been in units that countermanded base regulations many times. As long as the base doesn't word the regulation as "all members MUST carry", the tenant commands can modify the regulation to make it more strict.