I've followed the research a little bit. The general sense I get is that, specifically vehicle control at the edge of traction, software in the lab has far outperformed normal humans for over a decade. The problem is that delivering the "boring" point A to B reliably in all conditions is still unsolved. Relative safety is also a moving target because all the advances in the first bucket are directly applicable to human-driven cars as driver aids.
Yeah, my non-autonomous Toyota can already see the lane lines better than me in the rain. However, that's not too beneficial when no other driver can see the lanes and everyone is just driving to not crash into each other.
It gets real hard when the entire road surface is covered with snow for weeks at a time (like after small 1" snowfalls that might not get cleared immediately like a heavy snow would). Or when snow buildup on the road edges change road edge location and cars parked on the side project well into the "nominal" GPS derived lanes. Lanes which human drivers won't be using. They'll be using emergent lanes defined by flocking behavior. I haven't seen any evidence that autonomous vehicles can detect or navigate such emergent, non-marked except by tracks and human gut feeling lanes.
Being "better" than human in these situations will cause crashes. The real goal is to drive like a human.
