The year is 2062; man is able to lift heavy objects into space by using a massive elevator that spans from the planet into the heavens. The world is split into two superforces, one of which controls the elevator - causing tension between both sides. Kei Katsuragi is a Second Lieutenant for the Freedom Space Corps, and his mission is to destroy the elevator. But when something goes wrong with the Space/Time oscillation bomb, Kei is caught in the blast and tossed into another dimension. He awakens in a strange new world where he's caught in the middle between the Emaan, a nomadic people who rescues him; and the Chilam, a military force who want to capture Kei for their own unknown reasons. Kei must now journey to find a way to restore time and space, try to make his way home, and avoid being caught by the Chilam army.
Both of these series revolve around a guy who pilots a fighting mech unusually well and joins up with a caravan of people, acting like their knight or bodyguard. The protagonist in each story doesn't fit in well with most of the caravan, seeming more barbaric than the rest of the group, and seems to stick with them primary because he doesn't have anyplace better to go. These two shows really fell quite a bit alike, aside from the fact that Xabungle takes a more humorous approach vs Orguss's notably darker tone.