I can tell you from personal and anecdotal experience about Kyokushin and Enshin. Shidokan is something I only know of threw reading their site and seeing some examples of their sparring practices.
Kyokushin originally came from a Shotokan tradition and in its sporting context was meant as a straight forward shoot 'em up. Meaning punches and kicks...no grabbing or head shots...and no padding to attentuate these things.
Points are given only if the the opponent reacts to the shot...a good kick or punch that doesn't make the opponent react or turn away from the shot are not considered points. Though there is more "flow" (side to side and lateral movement) now a days from the earlier tournaments. The earlier tournaments were aiming to have folk move straight through each other and not move backward.
Enshin has similar rules, but allows grabbing and throwing and is noted for trying to move around the opponent to attack from the weakside (essentially their take on Tai-Sabaki) and thus the name of their tournament "The Sabaki Challenge."
Shidokan looks more like a tryptic paintings where there are three sections to a bout: 1) Karate (Kyoklushin style) fighting; 2) Kickboxing (similar to Muay Thai); and 3) Standup that goes to grappling. If I remember correctly the first bout is sans gloves. The second bout is with boxing gloves. And the third uses MMA gloves.
I could be mistaken about the gloves, but I have watched a few bouts here and there to something similar to this.