In a SHTF situation having a few of most common calibers would seem to make more sense. You would be more likely to find ammo if you had to "hunt" for it so maybe .22lr, 12ga, 5.56, .308, and 9mm. But, if SHTF really happened I wouldn't want to carry around a huge pile of guns and various calibers. I would probably bring two 9mm handguns, an AR15 in 5.56, 12 gauge Semi auto shotgun, and maybe a .22lr rifle and handgun.
But, what is much more likely to happen would be another gun ban scare. On that note having more calibers does make more sense to me. During the last panic it was (and still) is very hard to find many calibers of handgun and rifle ammo. I personally plan to diversify calibers some in order to be able to find ammo when I am out looking for some. This way if I can't find .22lr or 9mm I can still find .45, .38 spl, or .357 mag for example. Currently, I have guns in 9mm, .22lr, 5.56/.223, .308, .35 Remington, 12 gauge, 16 gauge, .38 spl, and .357 mag. In the future I could see myself adding guns in 9mm Mak, .380, 7.62x39, .45, 30-30, and .30-06.