I currently have a Honda Civic with lane keep assist. It doesn't slow down before curves and disengages frequently. Tesla's autopilot works much better from what I have seen.
I have a 2016 Volkswagen (Tiguan II), whose Lane Assist also leaves a lot to be desired. It handles nearly straight roads with no traffic quite ok, but it would surely crash the car on nearly every obstacle (lane narrowing/widening, obstacles, tighter corners, ...) without manual intervention.
That's a reason why I don't believe in seeing safe autonomous cars during the next few years at all. But maybe Tesla is that much better - haven't ridden one.