For a pure SHTF gun/ammo/scenario I would limit it to common easy to get calibers that you can get in bulk. Today there isn't much out there to get in the common 5.56, 7.62 Nato, and 7.62x39. You might have better luck getting the good old .30-06, but I wouldn't count on it.
Guns to consider are the AR type, AK type, lever action type, and perhaps a good bolt gun or if money isn't an problem an M1A.
Personally I would rather have...
However if you are limited in only the two calibers you list. I would go with the 7.62 over the .30-06 even though I love the M1 and cartridge.
An enlightened zeal for the energy and efficiency of government will be stigmatized as the offspring of a temper fond of despotic power and hostile to the principles of liberty.
Alexander Hamilton, author of Federalist No. 1. 10/27/1787