I find the difference between 1.1X and 1X a HUGE difference personally. 1.25X is even bigger and 1.5X... you know what I think of that.
Now you have to understand a few things about magnification, optical curvature of field, and how your brain works. I have a Meopta Meostar 1-4X. It has wonderful optical quality and is 1X exactly on the edge of the field of view. ALL optics have a curvature of field because you are looking at an image generated from a curved objective lens. Its kind of like looking through a very slight bubble. This is exagerated on a 1X optical magnification setting. While the Meopta is 1X on the edge of the FOV it more like 1.05-1.1X in the center of the FOV. What this means is that with both eyes open I can pan my rifle while shouldered and I do not have ANYTHING blocked by the scope housing. My eyes merge both views into a seamless 1X image that grows a tiny bit in the center which I still view as ONE image. Objects will transfer from your non dominant eye to your dominant eye and your brain will see it as a continuous, seamless image. There is no "jump" in size as the object moves from the non dominant eye generated image to the one through the optic.
This is NOT the case with a non true 1X scope. The only true 1X scopes I have tried are the Meopta Meostar and the Leupold CQT. I hear the Elcan DR and NF 1-4X arte also true 1X but have not tried them. Non true 1X scopes are things like the S&B Short Dot and the US Optics SN4 which are 1.1X... they are not seamless. Instead a non 1X scope is like a tiny low magnification circle in your FOV overlayed on a 1X background. As the image moves from the non dominant eye to the optically generated one it will almsot dissapear from view and "jump" into view at a larger size or appear to be a larger ghost image over a smaller image of the same thing. Its a non unified field of view. This is still usable but not as "ideal" as a real 1X scope IMO.
You are also going to have a magnification shift at close range regardless of magnification power. The image of your scope is generated from an objective lens several inches closer to the taget than your non domainant eye. This means while my scope looks like a 1X at 3m and beyond at 3 feet and under the image looks like it is "bigger" in the scope and the 1X "seamless image" effect is lost. As range increases this difference becomes so small you brain will quit registering it and you get the unified FOV again. That range starts at ~10 feet for my optic.
I hope this helps explain why 1X is "better" than a 1.1X to 1.5X minimum power. I think 1X is "ideal" for a dual role optic. However what is "suitable" for CQB is something that has to be decided by the individual shooter. You most certainly loose something by using a non 1X scope, but that may not be as important as the other features or magnifiaction you might give up with one particular optic vs. another.