I have seen in calipers that have set for a long time where the piston seal (quad seal) would stick to the piston and can get peeled up into the caliper housing jamming the piston into the caliper. If this is the case the hydraulics will be the best way (safest) to push the piston out of the caliper...

 

I completely agree that using hydraulic pressure to pop the piston out is the gentlest way to do it!!!!

However I'd still use air pressure 'cause I don't have the patience for the slow way.

Just take the caliper off, put it facing piston side down at the work table and hit with air and boom the piston is out.
There will be a boom btw!!!