Let my now say more
Roboat,
I deliberately keep my previous answer short, waiting for more info. NOW here is the rest of the story. I think what you are asking is "DOES OVERWELMING FIREPOWER WIN SIMPLY BY IT'S POTENTIAL." Short answer NO.
I said "caliber is not important" because you have chose in your nightmare to confront the boogie man with a .380. That is, what it is. Hopefully NOT ONE OF US would by choice go into harms way with a handgun of any caliber, we would choose something more substantial "like a 105mm beehive round", or a good battle rifle or a scattergun.
The problem is that living out side of a combat zone, in a world in condition white, it requires us to live with other precedences besides immediate survival. These other things (jobs, public perception, kids, distractions, in some manner even our own comfort) get in the way of our personal protection goals. AND THEN THE WORLD CHANGES FROM CONDITION WHITE AT PEACE, AND BECOMES CONDITION RED, (in the SHI_!). And there we are with a .380, and a predator with "a big old gun" 20 feet away.
Is that an adequate SITREP?
If so here is my answer,
Rule #1 In a gunfight, have a gun, any gun will due. .380 is a minimum defensive caliber, but we talked about that above.
Rule#2 In a gunfight never stop, never quiet, never surrender. The mere presence of superior firepower does not guarantee you will lose.
Rule#3 If it is time to fight, strike him first with as much firepower as you have.
At 20 ft with a small handgun and your hands trembling and epinephrine coursing thru your body, hits are going to be hard to get, my best advise is pick the biggest piece of meat and shoot the hell out of it, if that does not work reload and pick another spot and shoot the hell out of it.
Trust me, it is VERY hard to instantly ratchet up our souls to be savage and aggressive while living in the normal peaceful world, your survival will depend on how quickly you accomplish that, more than the power factor of the handgun in your holster. Be nice to have a couple of extra mags with this one, sometimes FerFAL is right.
Hope this helps
Good Luck, Be Safe!