Downsampled to 20MP and made the color balance of the A6000 more in line with the RX100, and added a modicum of sharpening (not a ton). If there's any remaining difference in the pixel level detail of this tree, it's minimal.
We tend to forget that 24 vs. 20MP is not equivalent, and I still say JPEGs are not reliable for lens clarity tests—Which is not to say you don't have a poor 16-50 with a flaw, or that they're not prone to flaws, or uneven clarity. That all may be, but based on this test alone I don't think we've established it. IMO, of course.
PS: maybe the 16-50 just isn't a 24MP lens at this aperture..?
PPS: Maybe there was some wind that moved the tree? I see some movement from one shot to the next in terms of the foliage, so there had to be some, at least. Heat distortion could also cause detail smearing...