Currently it is probably worse than the average driver. But here is a trolley problem for you. What is the ratio of people killed who volunteer to test out an auto-drive to the number of lives saved by that early testing? 1:1, 1:10, 1:100, 1:1000, 1:1,000,000? A million people die in vehicle wrecks each year.
The problem is that it's not just the drivers who are the volunteers getting killed. When you kill pedestrians as Uber did, they did not volunteer to be killed to test your software.
Yes automation is good, but Tesla is being needlessly reckless. They can easily be much more strict with the settings for auto-pilot but they're not.
If you are talking about the world a large part of that million are killed on the roads where no self-driving car would be able to drive anyway.
Also "normal" drivers do not usually get killed in crashes—unless it involves reckless driving. So probably self-driving is safer than drunk driving, reckless driving or driving on the roads with the extremely poor infrastructure, but compared to responsible driving?
Also, why is this so black-and white? The safest current option is technology assisted driving, but no much talk about it.
I'm just throwing something at the wall here: Just start with a purely assistive package like most big manufacturers have. Let buyers opt-in to a test program (giving them, say, a 3% reduction on the list price), where all their inputs and outputs are recorded and sent to the manufacturer. Manufacturer can now assimilate that data into a model of car and road and test their fully autonomous software on that model and search for situations where the software gave much different input compared to the human driver. Check these situations in an automated way and/or manually to see whether it's a software error or improvement. IMO this approach would have had a high chance to find the bugs that caused the two recent fatalities, as I'm convinced that most human drivers would have done better there.
After years of doing this (which seems to be close to what Waymo is doing if I understand correctly), the autonmous software should be way better than what is being pushed out now by Tesla and Uber (and probably a bunch of others).