I've ridden in a Waymo probably 10-15 times, and I felt like it drove completely safely, obnoxiously so, in fact.
During one trip, we were experiencing extremely heavy rain, and the Waymo pulled over for about 15 minutes until the rain calmed down. A normal cabbie probably would have risked it (and more than likely would have been fine, but it still would have been a risk).
The other thing is that Waymos truly obey all traffic laws and speed limits, which just isn't how humans realistically drive. I'm not saying they shouldn't obey traffic laws and speed limits (they absolutely should), but on average, a Waymo trip took about 20-30% longer than the same trip with an Uber driver. Again, I'm an advocate for safety, and so I feel like it's a reasonable trade off… but I wish there was some way to legally and safely have autonomous cars drive a few mph over the speed limit, when the cars around them are doing the same.
In any case, I'd be interested to see the direct tech comparison between the Tesla cab and a Waymo. I definitely feel like the lidar will give Waymo a significant advantage; I was incredibly impressed at how clearly the Waymo could see people and cars that I, myself, could not visibly see. It's really cool how they display that on their dash panel for passengers to view in real-time, and it adds a lot toward building confidence in using autonomous cars.