Reasons not to fill unused board area with power planes instead of ground planes?
As a rule, the ground of the circuit serve as a reference point for all signals. That is why it must have very low voltage difference across the circuit. It is generally not true for the Vcc - as long as no signals are measured relative to the Vcc, some bigger voltage differences are acceptable. 

The total current in the Vcc line is equal to the current of the ground line. But because of the above paragraph reasons, the ground line must have much lower resistance (actually impedance) than the Vcc line, where high inductance together with decoupling capacitors is even good.

That is why, the ground is often routed as an area, but Vcc simply as thick enough tracks.

This all was in theory. If your PCB is not dealing with high currents and/or very high frequencies, you probably can route it in whatever manner you want and everything will be OK. So, don't be paranoid. 

Footnote: If you have so big empty areas, isn't it better to change the design in order to make the PCB smaller?