Image sharpness comparison?

Hi, all - I am just getting back into ILC photography as a hobby after some 40 years. Back then we used traditional controls for aperture, shutter speed and setting the ISO on the film cameras. I decided to go with the Fujifilm X system due that same traditional approach to camera control, plus apparently good quality lenses, relatively compact cameras, the support and a user community that I really enjoy.

Now, I have this new X-T20 and the kit 18-55 mm lens that I am quite happy with, but I have two questions.

Question 1 - Image quality (sharpness) of Fuji X-T20 vs. Sony RX100-II

I have been comparing the quality of the photos from this new Fuji equipment with my old RX100-mk2 camera, and I don't see much of a difference in sharpness, if any, when "pixel peeping" on my monitor in Lightroom or other software. Is this normal? I would have thought both the smaller sensor and perhaps not as high quality lens would bring out some difference. I have compared various photos taken in similar settings - sometimes the Fuji has a slight advantage and sometimes the Sony does.

I set up a simple test inside, taking photos on tripod with both cameras at the same or comparable settings, f8.0, ISO 100, shutter 1/20 sec. and focal lengths 34mm (Fuji) and 21mm (Sony) to make the images fill equally up the frame. Keep in mind that the Fuji has an APS-C sensor while the Sony has a 1" sensor. I put the test image on a sheet of paper (A4, approx. letter size) about 1.50 m or 5 ft in front of the cameras. Here are the results from this small test (I hope you can zoom in for closer comparison):

Fuji X-T20 image

Sony RX100-II image

So, is this negligible difference in image quality (sharpness) what I would expect? Are there other conditions where the larger Fuji lens and sensor would excel?

Question 2 - Resolution of the RAW (or RAF) vs. JPEG photos

Here is a somewhat unrelated issue, but something I came across when doing this comparison. When examining RAW files close up (pixel peeping) in Lightroom, I sometimes found the resolution of the RAW images to be somewhat coarser than what I found in the JPG images produced from these RAW files. It surprised me, but perhaps the JPG interpolation makes its pictures look smoother and apparently have higher resolution to the eye? I did not manage to produce an example to illustrate this, but am I right about this?