Freeways are, in principle, much safer than roads with at-grade crossings. With postwar design standards, they eliminate the frictions that are responsible to a vast majority of accidents: grade crossings, left turns, opposite traffic (since they have medians by design), and so on. They also maintain higher design speeds and capacity than less safe local streets. But a more interesting question for policy purposes than “are freeways safer?” is “does the construction of freeways increase road safety?”
For some evidence that the answer is no, see PDF-page 3 of a John Adams paper from 1987 arguing for the continued primacy of Smeed’s Law. Traffic deaths per unit of vehicle distance driven had declined in both the US and UK at a rate following a multi-decade log-linear trend: 3.3% per year in the US, 4.7% in the UK. Regardless of whether Adams’ theory is correct, we can compare actual death rates to the trendline to see what happened. In the US, where the data goes farther back, the greatest period of freeway construction started in the mid-1950s and ended in about 1970; this was also a period in which traffic deaths increased, even more than the trendline based on the explosive growth in driving predicts. Of course the Interstate system also led to traffic growth on at-grade arterials, but the greatest construction growth was in freeways, and on top of this suburban sprawl meant more people would be driving on both the new freeways and the older parkways.