Is it healthier for a capacitor to be discharged to itself or to "ground"?
The only GUARANTEED safe answer is to discharge the capacitor, through a suitable resistor, across the capacitor terminals.

It is true that in most cases one side of the capacitor will be grounded and the other attached to some rail, HOWEVER this is NOT TRUE in all designs. 

There is no guarantee that grounding either pin of the capacitor to frame ground will discharge the capacitor. 

Further, by doing so you may actually be applying power to some circuit that does not expect it and can potentially damage it. 

It is also prudent to re-test after discharge with a suitable delay to make sure that some circuit on the board is not bleeding, or pumping, more charge into the capacitor.