Aren't a number of SUVs less safe than cars? Particularly, I seem to recall that cheap, top-heavy SUVs built on a car base (instead of a truck base) are way more likely to tip or roll over in an accident.
It is my understanding from anecdotal evidence that perception reins over reality in this case. SUVs do have a mass advantage so they were expected to win in a collision with a compact car. They also project ruggedness, which is equated with safety.
