(*firefighter here*): Yes. A lot.  

why?

- The **structure** is *much more stable* and deforms pretty much less in an accident (for example, cutting the struts of an old car takes 2-3 secs, a modern BMW about 15 secs).
- Airbags. A lot more, also on the side etc.
- Belt-release system that doesn't block completely and therefore decelerates you slower.

From my own experience as a firefighter (in the road rescue squad), this seems to be the main differences. Accidents still happen and car crumbles, but there is a **huge** difference between old and new cars (as well as cheap and "expensive" ones).

Just watch some videos of car-crash tests. You will see the difference;)