Panda I is rated at 7V to 12V
Panda II is rated at 6V to 9V.
It’s the sames voltage regulator, so why is it not the same voltage?
We use a 12V battery and a panda I, but we need to upgrade to a panda II.
12V will be fine on both boards as long as you do not add more circuitry that draws more power, which will cause the regulators to over heat.
From my own experience, don’t try for an example to stack a Fez connect shield on your panda using more than 7,5 VDC, it can heat very quickly ! If you want to use a higher voltage power supply, just use a small DC/DC converter that will convert your power without dissipating it into heat 
You will save your batteries life too !
I have a 12V to 5V regulator, will the panda work with 5V?
If you got regulated 5V then you can connected directly to 5 volt pin (not Vin)