If I shoot identically spined and weighted arrows, one a 23/64" wood and one a 9/32" carbon, the carbon will act weak due to it's reduced diameter (bow is tuned for 23/64"). I can't switch between the two without going lighter point weight on the carbon or building out the side plate as mentioned. I think that is at least part of the reason that so many people shoot a stiff 75/95 carbon, the reduced diameter requires a stiffer spine than normal wooden arrows of standard 11/32 diameter.
Just my 2 cents based off of my experiments.