Stripline (with target impedance) between ground and power planes?
My question: is it the same, for the purpose of characteristic
  impedance, to have a ground plane or a power (VCC) plane?


It's the same - Vcc planes are highly capacitively connected to ground planes and, if not, they should be. So, they behave identically for the calculation of characteristic impedance.


  Plus, even if it is the case: are there any requirements on the
  geometry or decoupling for the power plane(s)?


Yes, decoupling the Vcc plane to ground needs to be done at regular intervals along the length of the stripline. Probably (for best effect) at distances not greater than \$\lambda\$/10 but this can vary.