I suspect yes, notwithstanding Nick Chambers experience:
I rolled my Toyota Yaris three times this morning after hitting a six-foot-high dirt embankment at highway speed. I crawled out with no more than a bump on my head, seat belt burn, and a massively stiff neck. So, for all you small car safety-doubters out there, I’ve now got personal experience to say otherwise.
I’m glad Nick is okay—but I don’t buy that his experience demonstrates what he seems to think it does. There is a huge difference between the forces a car would experience in an oblique impact and roll, such as what Nick describes, and those it would experience in a head-on collision with either a stationary object or with a more massive moving object. And, of course, Nick may just have been lucky.
It’s not force that kills you in an impact, it’s deceleration. All else being equal, a less massive car should experience greater deceleration in a moving impact (given F=ma), and is likely to have smaller crush zones than a larger vehicle, which will logically have less energy absorption potential than a larger zone of equivalent construction. Furthermore, I would expect a Yaris on Escalade collision may well see the larger vehicle climb over the smaller one, given the relative offset of the respective bumpers, further enhancing the risk of trauma. Finally, see this study (PDF), which finds that you are, in fact, more likely to be killed or injured in a less massive vehicle.
There may be many good reasons to buy smaller fuel efficient cars, but we should be aware of the trade-offs we’re making.