Your dilemma is artificial.
Either gun is likely to be all you need for home defense given that well over 90% of self-defense gun uses don't require the intruder to actually be shot.
Something like 8 or 9 out of 10 self-defense gun uses don't even require a shot to be fired--the attacker retreats as soon as it becomes apparent that the defender is armed.
Of the incidents where a shot is fired, the majority are resolved favorably even if the intruder is missed entirely or only slightly injured.
In the event that you are actually required to break an attacker down, a single round of good defensive 12ga ammunition will do the trick if properly placed. Similarly, a good 9mm defensive round is also quite effective if properly placed.
The combination of the two should be more than adequate for virtually any scenario providing the person wielding the firearms is up to the task of making good hits under pressure.
Choosing different calibers and/or weapons won't alter that analysis significantly.