Here's some of my initial findings regarding the K3iii using various lenses. I've tried the following thus far: DFA 150-450, DFA 70-200, DA 18-135, DA* 16-50 SDM, DA35 f2.4 FA 28-200, Sigma 105mm macro.
All of the DA lenses seem to focus nearly equally well and with nearly a 100% accuracy! In every case I experienced I'd attribute the misses to the photographer. I tested the DA* 16-50 SDM at f2.8 with excellent results.
The Sigma and the FA 28-200 are both screw drive and I found they are not capable of reliably keep up with quickly approaching subjects. The Sigma was maybe 50-60% keepers while the FA 20-200 was mostly unusable for fast action.
My opinion is based on 50 years of experience starting with the K1000 and MX. Digital starting with the KR, K5ii,K5iis, K3ii. I've never used the K1 or K70 and know they each have improvements over my K3ii experience.
I cooked up this photo taken with the K3iii, DA* 16-50, 1/4000 sec., f3.5 at 50mm.