I shoot wood. Some of my shooting buddies shoot aluminum and carbon. Would probably be small differences for a number of reasons. Even at the same spine, the physical weights of the shafts/arrows will be different, affecting the dynamic spine. Also the shaft diameters will likely be slightly different as well, which affects how how closely the center of the shaft is to the arrow plate, i.e., the initial orientation of the shaft in relation to the bow sideplate and thus the amount of flex required to bend around the sight window -- the thicker the arrow, the greater the flex required. I also feel, but can't prove, that the three materials are just inherently different and flex ever so slightly differently.
Just like with woodies, you need to experiment with a few different size, weight carbon or aluminum shafts to find the best one for you. Good luck.