One of the biggest concerns people have with buying smal cars is crash safety. More specifically, there are concerns about what happens when a small car meets a larger one in an accident. Regardless of size, all cars are required to meet the same crash safety standards. The problem is that crash tests are done by slamming a car into a standardized barrier, while accidents in the real world don't generally involve impacts with standardized barriers.
When cars of different sizes collide there are a huge number of variables that impact the result. One of those is kinetic energy, which is a function of mass and velocity. A larger, heavier vehicle has more energy than a smaller, lighter one, and in combination with less crush space, the latter tends to come off worse in an accident. The Insurance institute for Highway Safety has run a series of crash tests between sub-compact and mid-sized cars and in all three cases the small cars did substantially worse than they did in the standard crash tests. All of the small cars earned good scores in regular testing but did poorly in the new tests. The IIHS press release explains the results after the jump.