"Stopping Power"- There is no denying the .45 is bigger, but all in all, most pistol calibers perform near the same when using high quality ammo in regards to terminal performance. A hit to the vitals with either will stop someone. A non vital hit with either wont.
Weight- 9mm is lighter, you can carry more
Capacity- In Hawaii we are capped off at 10 rounds either way. But the 9mm wins in capacity if you are somewhere with no mag limits
Recoil- I find the .45acp to be fairly soft shooting. But 9mm still wins this round.
Ammo resources- In any SHTF, emergency scenario etc.. there will be no such thing as ammo resources. Only expect to have what you have already stocked up on. At some point, people began thinking that you would just run into common calibers during an emergency. This just won't be true. You wont be bartering for ammo, finding caches or anything of the sort. You will only have access to what you, and your immediate group of friends and family (if they are part of your shtf group) have already stored. So its a moot point either way.
Price- 9mm ammo is almost half the price of .45acp. That means you can stack it deeper, and train with it more.
Lastly, I think that in the event of true SHTF, a rifle is going to be a much more capable weapon either way.