The 3 and 4 vane spiders put visible diffraction spikes on bright stars (the diffraction spike just isn't bright enough to see on dimmer stars but it is there) while the curved spider systems don't.
Please note that any edge in the path of the light produces a diffraction of the light coming in. The intent of the 3 vane over the 4 vane is to decrease the amplitude of tho visible diffraction and it does to a degree but it adds in 2 more spikes than the original 4. The curved spiders avoid the spikes by making the diffraction curved and thus just make the background to the star area a little brighter than it would otherwise be. The energy is going to go somewhere in the image and the basic difference between the various methods is where in the image that energy is going.
I'll note that there have been wars done over which is better but it more ends up being a personal preference to the viewer.