Stastically, most fire fights are at very close range and only contain a few rounds. This means that basically having a 5-shot .44mag would probably be best.
But then when you add in other factors (as mentioned such as multiple attackers, greater distances requiring more accuracy, etc), the 9mm wins overall.
Pistols built around the 9mm have much higher capacity than those built around the .45 (typically 17+1 vs 12+1), while the best 9mms statistically only have a few % chance lower to get a one-shot-stop. So, ultimately by going 9mm you are losing about 5% in "stopping power," while gaining about 40% in capacity.
Also, the lower recoil of a 9mm will mean greater precision for most, which will be paramount at larger-than "give me your money" distances (across the street or even across your living room, for example). Being able to recover and retarget more quickly between shots could be important.
There are, of course, other more nit-picky advantages like the lower cost allows more practice (and if you don't practice, you won't be able to hit what you aim at, and if you can't do that, then the whole gun thing is a moot point).