Completely agree it's hard to say what is right for another person. But honestly I think if you don't have access to at least a weeks worth of food, gas, and other misc expenses you are very unprepared. A couple week's worth of cash is a pretty good amount of money to have laying around so I feel it's important to also have a safe place to keep it. But if you own guns odds are you already have a place safe enough for your cash.
A tornado is one of the ways that can really mess up the banking system in a local market. Without electric banks are dead in the water. No ATM's means those who are unprepared have no means to purchase anything. Also in a case like this you need to be ready to price gauging so your typical price for gas will jump drastically, along with water and other essentials. Even more reason to have plenty of cash on hand.
People were driving 60 to 70 miles away to find gas and ATMs when the tornadoes hit here. It's great that a bunch of people could get out that far, but how many people always have less than half a tank of gas? It really is crazy what a stash of cash will do for you.