Put her on a tripod for the most control possible and see what you get. I'd even use remote trigger if you have one.
The mkII is definitely not softer than the 200 f2.8 L II, and for all intended purposes IS helps to get a sharper image. Personally I have never once gotten a sharper image without IS than with.
I find that IS does not give the sharpest image. If you're testing the lenses against each other, then use the same technique. Use a tripod if you can and if you're handholding, disable IS to make it comparable to the prime. IS reduces camera/lens motion but it doesn't eliminate it.
The 70 - 200 does look a little soft. Although I think you need to do a more scientific comparison between the two. Use good lighting, a tripod and make sure the ISO (the 70 - 200 shot seems noisier to me which doesn't help sharpness either) is fixed at 100. You should also disable IS (just to eliminate all variables).
Do you notice a big improvement when stopping the lens down?
Tested again this morning.
-IS is set to "off" on the 70-200
-Tripod used w/ 2-second self-timer
-Focus set to center of chart
-exposure settings are the same
-manually focused using Live View on EOS RP, did 2 trials of each setup, then selected (and have included) the sharpest images
-stopped down each lens to 5.6, as well as tested wide open at 2.8
errors:
-had to move the chart between test setups because the light changed
-
I didn't test this, but I know my copy of the 70-200 is much sharper below 135mm than it is above 135mm.
Is there something wrong with this lens? I'd like to sell it, but now I'm second guessing doing that out of fear that someone who buys it will think the lens is no good.
prime @ 200mm, f/2.8 (full view, 1:1 view)
zoom @ 200mm, 2.8 (full view, 1:1 view)
prime @ 200mm f/5.6, (full view, 1:1 view)
zoom @ 200mm f/5.6 (full view, 1:1 view)