All handguns are relatively poor "stoppers" regardless of caliber or bullet used. Shot placement and sufficient penetration are paramount, all else is secondary.
Expanding bullets? If you carry a load that's capable of sufficient penetration *and* expansion then the additional damage can only increase the bleedout rate that leads to incapacitation due to drop in blood pressure and oxygen deprivation to the brain. In general this is a good thing.
However, there's no scientific way to prove if this expanded bullet will increase the bleedout rate enough (seconds? minutes? hours?) to alter the outcome of the encounter (doesn't do you much good if he passes out from bloodloss in the ambulance from JHP's instead of the ER from FMJ *after* planting daisies in your hair).
I follow the conventional wisdom of carrying the most powerful caliber I can shoot both accurately and quickly w/quality expanding bullets (except for .380's where it's FMJ only as sufficient penetration trumps expansion every time) but don't believe that expanding bullets will significantly increase the chances of my hits ending the fight (YMMV).
"Among other evils which being unarmed brings you, it causes you to be despised." - Niccolo Machiavelli