There really isn't style vs style match ups anyway at this point, not in the sense of BJJ vs Catch Wrestling. Barnett was trained by Erik Paulson, a guy who has trained under lots of top BJJ guys and added some other stuff to it. So Barnett trains BJJ and with BJJ guys constantly, regardless of calling it Catch Wrestling. Everyone else has trained with Judo guys, Sambo guys, etc.
The only real style vs style that is going on is a person's individual style and preference. Some are guard pullers, some want the takedown, some are great on top. Some guys come from the sport BJJ scene and use all of the crazy stuff, some are more traditional.