Flying a spankin' new 320 in moderate turbulance (almost every day) I tried a few times to leave everything hooked up. AP and AT. The last time I hit 2000 fpm at 1200 AGL. That was the last time I let the airplane fly in similar conditions. With me flying in the same conditions, I keep it within 200 fpm of target rate of descent, and closer on airspeed.
When conditions are smooth, I can't even come close to the accuracy of the aircrafts systems. But when the going gets rough, the organic stick actuator is better.
I also flew MSN 300-311 3 years ago. But in much more benign conditions. I don['t know how well they would do.
Airbus autothrust is really good. Much better than Boeing, including the 777. But lookup the limitations of the basic aircraft. Then look up the autoland limitations. The aircraft is much more capable with YOU operating the controls than the built in automation.