In my home town there was a car dealer who ran a commercial where
a compact and a Cadillac were in a head on collision, and as you can imagine, the compact lost. One of his competitors who sold compacts retaliated by running a commercial showing a Cadillac getting hit by a train. I think he made his point.

All else being equal, the small car will always lose to the big one, that's just physics. But all else is not equal. Small cars maneuver more effectively and stop faster. And if they are properly sprung and have good steering geometry, they are less likely to roll over or lose control. In other words, small cars are less likely to get into an accident in the first place. They are also, by definition, smaller targets. The subjective feeling of safety you get in a big machine is just that. I've always driven subcompacts and I feel much safer in them, because I know I have a better chance of avoiding a collision or maintaining or regaining control on a slick road. Besides, in today's world of monster trucks and SUVs, it's getting harder to find any sedan that can survive a collision with these behemoths. This, and the difficulty drivers have seeing around and over them, make them safety hazards to everybody else.

Experience on the race track, where drivers routinely survive horrendous high speed crashes in cars of all sizes, from Nascar to Formula, suggests that the technology already exists to make cars much safer, not just by retrofitting extra devices, but by designing them from the ground up to be safer. Car size has nothing to do with this.