It really is hilarious, especially on a vertical surface. They use every trick in their repertoire to gain the advantage. They often use their safety lines, sometimes jumping over the other spider and landing behind it. Since the combatants are usually so equally matched and their eyesight so acute, reacting to the slightest movement of the other, most of the time neither gains advantage and they just go round and round.
They appear to need to establish a given hunting territory first, and even then don't rigidly defend boundaries. Once one has patrolled an area it will face off other jumpers. Whether this is a territorial dispute or simply a pair of equally matched predators could be debated.
I had one that insisted on patrolling my computer area. For about a month it would spend about a half hour trying to catch the mouse pointer on the screen, walk the perimeter of the monitor, and when I accommodated it, it would patrol the keyboard. It finally got so used to me it would walk the upper edge of the keyboard while I typed.
Poor little fuzzhead!!