The sidewall stiffness, rim width and air pressure make the difference in feedback and response, not the diameter of the wheel directly.
That is one reason why I always recommend a slight stretch on the tire, most 205's are better on an 8" rim, 225's on a 9", 245's on a 10".
As in all thing we need to find the right balance firmness, sidewall support, run the right air pressure, etc....AND we need to ensure the real specs are considered, not sidewall specs, actual section and tread width, diameter and weight are all important including the class of the tire and feedback from knowledgeable users and professional testers and racers.
A tall, wide, tire on a narrow wheel will certainly be more "squishy" feeling though could have a lot of grip.
A shorter, narrower tire stretched a bit would normally ride firmer but still offer a better ride in 15 than 17" in the same tire and can have great feedback and control.
The 225 Rival S is known to have a bit softer sidewalls than some performance tires, firmer than normal tires for sure, my 225's on 9" wide wheels are a great balance of huge grip, great feedback and ride hugely better than 17''s and far less noisy not just in tire to road surface noise but in the energy transfered into the chassis noise and vibration(same thing just different frequencies involved)
The new Rival S 1.5 was designed to make up a bit of the difference over the other ultra grip tires, stiffer sidewalls.
The Rival S is primarily an autocross tire and many classes force the use of less than optimum wheel width per tread width (sidewall markings, which vary greatly to allow use of much more rubber on the ground than a specific formula would create). Making the sidewalls stiffer will help out greatly making the tire more competitive in more classes.
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One thing I did not mention clearly is the lighter the wheels and tires besides better in every aspect of performance, ride and handling, less chassis wear, is the grip is increaded as well due to the tire staying on contact over bumps much better.
When really getting into the fine details of suspension setup as in all out racing this means one can run softer springs and damper settings to help even more, stiff means bouncing the tires off the surface causing loss of grip, softer suspensions keep them planted.
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I run 9k front and 8k rear springs with my dampers on mid settings on the street, much firmer on track, the Swift springs can be firmer as more linear and precise in their response to the road surface, they help control body roll enough I only have a stock front sway bar with stiffer bushings and adjustable end links(to remove and preload from side to side)
A little body roll is OK as long as it helps promote tire contact, two stiff of springs or sway bars, tires, lowered to much all contribute to loss of contact thus grip.
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A bit off topic but this may help explain my passion for light weight wheels and proper tire sizing as it is a huge part of my successes.
Over the decades I have beaten hundreds of cars with big budget builds that simply were not setup properly and the causes were most often in wrong tire and wheel package, springs to stiff, big killer is a car lowered to much, alignment, etc....
My particular Fiesta was not setup to race against similar cars in a particular class, it was built to take on exotic cars on road race tracks, not to beat them all just to keep up well and then let the drivers decide the results and most owners of such cars really do not know how or are afraid to push the limits of such cars. It is far more fun the come in right behind a super car in an "underdog" car than beat one in another super car, anybody that can drive can do that, not a real challenge in HPDE and at many levels in autocross.
Autocross, I build my cars they way I want then run whatever class they fall into and usually the wrong car but I can beat nearly everyone no matter what they have or have done to it, 2nd and 3rd places are great to achieve in fast classes where none would even consider my cars a contender
Road course, same thing but I just run HPDE and sometimes TT events.
I look at all the cars and run against them all in my head, not really concerned with placement in a class most of the time but it is still a fun aspect. I set top time of the day in a 500 car autocross school once in a Toyota Matrix, that was FUN