Some cars are rear wheel drive, some are all wheel drive. Many expensive cars require a flat bed tow truck. Cars with double clutch transmissions do not have a "neutral" setting and cannot be easily towed (when you put a BMW DCT into neutral it becomes park, for example).
If towed in the wrong way, it can severely damage an expensive car, and considering Ferrari owners can also afford lawyers, it's safer to tow the Civic, especially the towing fee is the same either way.
Every time I see LADOT towing a car it's on a flatbed, they don't literally tow it behind some other car. I imagine it's cheaper to use a flatbed if you are in this business.
Just a couple guesses, but sportier cars will have less space between the ground and the body, making it difficult to raise them at an angle or pull them up a ramp onto a tow bed. They would also probably have more sophisticated anti-theft measures.
