What difference is there between stabilizers and stabilators concerning longitudinal stability?
There is no fundamental difference between them in such context. If you don't go to the extremes like 90° deflection (and generally stay in the linear range), you can mentally replace an elevator with a stabilator at a different equivalent angle. All-moving surfaces are typically a design solution when additional efficiency is required for whatever reason.

There are finer effects, especially at supersonic, but they don't change the overall picture for 'normal' aircraft. You can always find border cases when, say, elevator will stall but an equivalent stabilator will not yet, but they will generally be beyond the operational envelope.

Stability is primarily determined by derivatives, i.e. the way moments change with changing angles (of attack in this case). Absolute angles (tail vs wing) are less important and are usually the consequence of the desired derivatives.