what makes a chord feel "resolutive" ?
It is our expectation of consonance and stability. The leading tones in a progression
are provoking the dissonance and evoking the tension for resolving.
if not consonance, what actually makes a chord be stable?
It‘s actually the consonance! But in Jazz a major 6 or maj 7 chord are considered as stable (at least as final chords).
In traditional western music the sixth ajouté was considered as a consonant chord like the dominant V7 (even the latter has a great tension to resolve the tritone fa ti => to mi do.
So it depends of the function and the chord progression. As the V - I is dominant functionof the tonic this dominant chord so ti re wants to resolve to do mi so (g b d to c e g).
Even that both chords are major triads it is in functional listening and thinking logical to say: the triad of the dominant chord is less stable than the tonic.
While a tonic chord e.g. C maj7 is less stable than C6. The ear that isn‘t schooled listening to Jazz is expecting that the 6th will resolve to the 5th and the 7th to the octave. Now the tension of the 7th is greater than the 6th because of ti as lead tone and the minor second is more dissonant.
I hope you understand that there is a correlation between consonance and stability and that it is depending additional of our listening habits.
My explanations above are referring to major chords.
Your question is concerning minor chords with added 6th and 7.
In this case I‘d leave the theoretical background of functional theory and dissonances, I can only refer to my own personal listening habits: as final chord I‘d hear am6 as more stable than am7, as passing chords they are both similar unstable to me.