Kuwabara's sword can cut through dimensions. That's a buu/ super saiyan 3 level feat. Krillin may have a technique advantage but that's unclear as the turtle school focused more on upping your stats than flashy techniques. Thats Crane school nonsense.
His dimensional sword cut through seaman's monster(who seaman says acts like another dimension) and then cuts his way into the demon world to fight sensui.
Kuwabara can cut through dimensions, but it's not like he's jumping around doing it easily, like he uses it once too to teleport and get the drop on some jobbers but other than that he doesn't get too fancy with it.
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One of Seaman's abilities functions where the inside of that water that his opponents are trapped in, resides in another dimension. Basically Sensui wanted to find the guy who could defeat this ability because he needed a way to cut open the barrier inbetween the normal realm and the demon realm, it's convoluted but you all get the idea. (please log in to view the image)(please log in to view the image)