If we get bombed back to the stone age you'll have much more to worry about than whether you have a running vehicle or not and bare survival will not leave much room for fun.

Carbs can be a pain. They need period adjustment, and rebuilding every once in a while. Over time and mileage problems can develop with the carb body. On the other hand, most are easy to deal with using simple hand tools and an inexpensive rebuild kit. For the most part it will be older and retired mechanics who know how to deal with carbs but I know a few younger ones into old cars that know how to work with them.

Fuel injection is more precise and needs less maintenance. In fact my daily driver is 28 years old and well north of 370,000 miles and the injection system has never had to be touched other than filter changes. Ditto for a fuel-injected car I have that is nearly 40 years old with 300,000 miles.

Of course you could elect to purchase an older vehicle that has mechanical fuel injection, particularly an old diesel which can be modified to run on waste oil. A friend of mine did that with an old Volvo diesel years ago and ran it on fryer grease discarded by restaurants. It smelled like French fries when he drove by.

Per usual, I agree with @chucktobias that getting suitable fuels might be as much a challenge as keeping the chosen vehicle operating. I'd consider getting an electric bicycle and solar cell setup if I was worried about societal collapse. But judging from history, the technological stuff usually survives much better than the organic stuff, like humans.

Another problem with carburetors is if you're dealing with a 1980s-vintage vehicle equipped with a carb the emission control system required to meet the standards of the day was crazy complicated. Check out the vacuum hose diagram from under the hood of a carbureted 1986 Honda Civic - have fun finding vacuum leaks! (In contrast my 1986-vintage fuel-injected vehicle has nothing like this.)

It's definitely not for everyone.

When I got my '79 Pontiac, I thought it was going to be like any other car, I put the key in the ignition and cranked it over; it wouldn't start. My now-father-in-law was outside with me and he said I need to pump the gas between 4 and 6 times before starting it. I pumped it 6x and I flooded the engine. Haha. He then told me to hold the throttle at WOT and crank it over until it started. It eventually did. Carburetors at their heart are basically gigantic lawn mowers; most lawn mowers need primed (you press a rubber pad few times) before starting. You need to think in terms of that. 

My father-in-law has a 1960 AMC Rambler, and that's one of the only cars that I know of where you don't need to prime the engine before starting it from cold. It was pretty advanced for that time. 

I got starting the Pontiac down to a science, and starting it in subzero weather is no problem. I got the carburetor all tuned up, though. I enjoy working on that car as a hobby. 

You can use almost anything that's flammable in ratios similar to gas and the car will start, if you're in a pinch. When I fired up my Pontiac for the first time, it started and ran on the 5-year-old gasoline that was still in the car. An EFI car would probably trip the CEL at least, if not run at all. 

Posted by: @alex-g

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It's basically the opposite of the simplicity I thought they were.

It really all depends on what era you choose as to whether or not carburetors are really complicated or not. The '86 Civic has analog emissions control systems, which require complicated vacuum hoses. My father-in-law's Rambler, on the other hand, is pretty basic. One notable exception I think is the windshield wipers are powered by engine vacuum, not an electric motor. I don't know the specifics of that, though. It doesn't have an EGR valve that I'm aware of, no catalytic converter, no evap canister, etc. All of that requires engine vacuum. 

My 1979 Pontiac has a similar emissions control system to the '86 Civic, as far as EGR valves and such. I bought the factory service manual off of Rock Auto when I bought my Pontiac. The vacuum hoses were all screwed up when I bought it. All I did was reroute the vacuum hoses to their proper places using an engine diagram with vacuum hose routings. I have a minor in mechanical engineering, though so that kind of thing is my forte. 

Wow, that drawing is crazy. It's basically the opposite of the simplicity I thought they were. I think I'm convinced to stick to EFI. I probably would have tried to track down a 1FZ-F engine in the J70 to J80 (I think) Land Cruisers but to even find one with low miles from the countries they were sold in if likely impossible these days anyway.

Yeah, think I'll stick to the EFI. Maybe a lead lined garage 1' thick or so might keep the EMP out. 😆