IQ difference? Maybe. Probably a bit. I haven't done controlled testing. I think most reviews and controlled tests, etc. lean towards the 28-200 being "better."
context - I noticed a fair amount of improvement going from the NEX6 and 16-50 to the A6400 and 18-135. I noticed less difference adding the A7Riv and 28-200. So, 2.5 years or so without using the A6400 or 18-135 much. I still notice the larger. heavier side of the kit. I've also become more comfortable/adventurous with post processing and the various programs have improved, too. Especially in noise reduction and sharpening. So, when I got the A6700 recently, the 18-135 went right on. Yes, it's still lighter! But I like the looks of what I'm getting from the A6700 as well.
I'm not a pro. Not an event, portrait or wedding shooter. Not a lot of prints. sharing is online, often Facebook these days, so things are processed, down sampled, and FB works whatever magic they do and family and friends either don't see IQ problems or are polite enough to not say anything.
I do think, if one is looking to a smaller, lighter, aps-c kit and has similar subject interests as I do, I'd have no trouble suggesting the 18-135 on Sony aps-c.