When the 70-200 f/2.8 L came out the non IS version was sharper than the IS version. I would suspect this will always be true no matter what focal length.
I am with you on that ... partially!
Canon introduced the 70-200 f/2.8 IS II which corrected this!
However, it has done this by almost doubling the cost (compared to the non-IS lens)
By the way the 70-200 2.8 L (which I used to have until it was stolen) was the first zoom I used with fixed lens quality (judging from large B&W prints back in the 90s).
For now, your comment applies to the 300mm f/4 series lenses too.
The f/4 non-IS lens is reported sharper than the IS version. Although I do not have the IS version
I have compared 300mm f/4L non-IS lens with EF1.4XII extender and found it sharper that the 100-400 L lens. This implies a very sharp 300mm f/4L non-IS lens. Now, if Canon introduce a 300mm f/4L IS II things will change again...