This summer, I took the a6000 with the 16-50PZ with me on my holydays to Ireland.. no problems with the image quality, especially when stopped down a bit to f8.
Some major issues however popped up:
First one was that at some point, there appeared a large thread of lint on the sensor. Mind you, that was with a camera where the lens hadn't even been taken off once since new! Shame on you Sony! The image cleaning option is a joke (shame on you Sony, again!), so with the rocket-blower safely stashed away where I couldn't get to it, I had to resort to a puff of breath.. worked out OK, but it's far from the recommended procedure..
Second issue was the Auto-ISO. Turns out that there are two Auto-ISO's, one ordinary one, and one where the a6000 takes multiple shots. But given that I also saw multi-shot under the scene modes, I couldn't figure how to cancel the multi-shot there for days; nearly threw the thing off the cliffs out of frustration. Talk about a convoluted mess of non-informative lock-outs.
At some point, the on-off switch started working the reverse way around; turn the camera off and the lens extended, while the EVF/LCD went black, turn it on and the EVF/LCD came on but the lens collapsed.. WTF? Seems like switching off and immediately on again can cause glitches.. was restored to normal after popping out the battery while switched on.
My conclusion, the 16-50 isn't bad image-wise, but I'll probably drag the Nikon along next time..
