Both.
You've got claims which can be resolved by any court of competent jursidiction. You will find that enforcing judgments interationally is extraordinarily expensive. If the corporate officers of Mt. Gox leave the country with their assets, then your judgment will be worth approximately the paper it is printed on.
If you're asking whether the Japanese government is going to backstop your deposit, short version: "No."
From the perspective of Mt. Gox creditors, the actor you most care about right now is probably an anonymous midlevel peon in the bowels of the risk department at Mizuho. The action you should pray he takes is freezing substantially all of their account value above that required for day-to-day operations, pending instructions from competent authority as to what to do to with those assets.