LJ - as ever in the modern world it's never straight forward.
As I understand it:
Aircraft belong to Army (JHC)
Costs of people (eg salaries and T&S) fall to Army (JHC) (for now).
Land and buildings and cost of maintaining them fall to DIO
All other costs (eg utilities, aviation fuel) fall to Army (JHC)
Full command of RAF personnel on the 2 stations fall to Air (1 Gp) (I believe that this may also include acting as higher authority for discipline).
I guess the bottom line is who gives the 2 stn cdrs their TORs and writes their OJARs.