Unfortunatly, I can not comment yet, so maybe someone can move this to the comment section.
I don't think, this statement is generally true. It depends on the inductiv and mesomeric effects of the side groups (+-I/+-M).
You also have to choose, what you mean with stability. The energy that is needed to break the doublebond or the reactivity of the double bond.
If a doublebond has four substituents (which are not Hydrogen of course) any reaction on the double-bound is stericly hindered. When there are still Hydrogens on it, the doublebond might be more likly to react. That doesn't mean, that it requires less energy to break the bond.