Question

What provides greater stability to an organic compound hyperconjugation or resonance

Answer 1

First one must realize resonce is shown for two reasons: 1) a structure is neutral with no charges and you are showing resonance charge separation to see why the molecule reacts the way I does. 2) your molecule has a positive or negative charge (or a radical) and you are drawing resonance to stabilize the charge that already exists. 

In terms of starting with a neutral structure if you can have the structure without charge separation (no formal charges) you are better off. 

Answer 2

Answer:

Since resonance facilitates delocalization, in which a molecule's total energy is decreased when the electrons occupy a higher volume, molecules that undergo resonance are more stable than those that do not.