We don't drive with just our eyes. We fuse vision, sound, touch and proprioception. We self-locate easily. Most important though, is we do sophisticated visual, theory of mind and physics based inference.
If you take the example of Chess, humans and machines play very different styles. Computers replace predictive understanding with excellent memory and fast search.
Similarly for cars, we want to replace the lack of a powerful predictive model with some compensatory mechanism, such as sophisticated sensors. The problem is that, even with faster reaction times, better sensors and fuller awareness, these cars' compensatory abilities against a lack of powerful predictive models are still far from sufficient.
At this point in time, a car with more sensors and failsafes to augment the human against collision is safer than a self-driving car that depends on a lack of lapses of attention. That depends on proper behavior in the customer. Even dividing tasks, with the human controlling the steering (but allowing the car to takeover when highly certain of danger) and the car controlling acceleration would be safer. This set up acknowledges the human propensity to mind wander when attention is not engaged.
Until self-driving cars no longer require human rescue in difficult situations, one can't rightly say that self-driving software are better drivers than humans.