I think this is another right tool for the right job question.
f you are worried about a E&M pulse, either from the sun or from a Nuke, then you are looking at vehicles from the pre-electronic ignition/fuel injection days only, or you plan to keep a spare car computer in a Faraday cage somewhere. However, even if you did, you become a really stupidly obvious target because your vehicle is the only one moving, and you can't move fast because every road everywhere is choked with abandoned vehicles ( unless the pulse comes at 3am) and scared people. In that case, you are still probably better off hoofing it so you don't look different than others. Granted you could also try a 3am run and hope no one notices. If I had millions, I would prep this this. I don't.
My main concern for a bugout vehilce was its long term use. Some way you will get to your teotwaki hideout. Car, train, hiking, biking, horseback. Once there, its probably rural, and you probably need a reliable means of transportation.
If you are worried about an oil/gasoline shortage, having a vehicle that accepts and alternate fuel is a good idea, and there are pros/cons to each type. We still have plenty of natural gas here in the States, and that is probably the best alt fuel to run on other than gasoline, as it will probably still be available during a gasoline shortage. However, it assumes you have some way of filling it up easily where you live, and outside of an urban area, that is going to be unlikely. Diesel will probably be in the same boat, since it can be made from various organic oils, but you are looking at much higher prices at the pump in the meantime. A "flexfuel" vehicle will let you run alcohol and gas, letting you use gasoline while available, and alcohol when not. You know humans will ALWAYS produce alcohol. Most states already require alcohol to be added to gasoline, and therefore much of the required infrastructure is already in place - alcohol just becomes more of the mixture. Further, a CPU addition
or some modifications
and most non-flexfuel cars are upgradeable to alcohol. Because of this, I would expect alcohol to become the liquid fuel of choice of most people if gasoline becomes to expensive - just as it was the fuel of choice before we manufactured gasoline. Old Model As has a switch to convert from each and most farmers made their own from failed/bad/rotten portions of their crops to run tractors etc. It is possible for individuals to make both diesel and alcohol, but diesel requires more steps, equipment and know how. For all of these reasons, that is the tech we placed out bet on, for good or ill.
Then of course there is the "gassifier" approach
where you distill wood to get methane and H2. Its probably okay for short trips, but its seriously a mad max technology. We talked about this tech for power generation
before. The problem of course is storage of the energy produced. H2 is hard to store without liquefaction, and you need serious pressure for that. Yes it will work , but it takes more to get it going than going out and turnging the key. Of course electric vehciles can also be used, but the battery tech will last you 5-10 years and then you are stuck.
Of course you probably need a 4 wheel drive or a motor cycle to get around obstacles, go off road and deal with blockages. If you have the money for a unimog, go for it. Otherwise, choosing something more standard may make more sense. However, the best teotwaki bugout vehicle is a set of horses, mules etc. They can go nearly anywhere. Their fuel grows nearly every where on the way to your destination, you can put them in a train to carry almost anything you want, and they can go over rough terrain better than any vehicle. Of course, you have high expenses maintaining them till you need them.