If your system is voluntary, in both funding and participation, then it’s no different than mine.
If not, mine is better, first, because it is not a system. Not one system imposed on everyone, it is a set of principles under which any number of systems can be designed and freely chosen.
Second, your system initiates force, not incidentally, but as an inherent quality of what you are proposing. Mine does not. Even if the worst happens, and the parties resort to violence, there is still no initiatory force involved beyond the original crime. Yours leaves the possibility that both parties end up wronged.
Third, your system creates a market distortion. It masks the true cost of not coming to a peaceful agreement, making the court of last resort more likely than the violence of last resort in my system. Market distortions lead people to make bad decisions, because they are deprived of the information needed to make good ones.
Fourth, it concentrates power in an unaccountable body.
Fifth, it issues fiat decisions. Even if the decision is the correct one, it is still fiat, since the judges are not subject to market forces, therefore are deprived of information needed to render a sound verdict.
Sixth, it is a magnet for people who prefer to work outside the constraints of markets.
Seventh, the judges will have to be chosen politically, since there is no market-constrained entity with the responsibility for making correct choices.
Eighth, it is a monopoly, being unconstrained by market forces.
Ninth, it distorts the market in another way, in that it will cause people to devote resources to influencing the court rather than producing value to trade with others.
Tenth, it creates a commons.
Eleventh, it will require an administrative branch to enforce its decisions, otherwise it’s completely pointless.
Twelfth, it’s distorted, misinformed, force initiating, collective, fiat, political, monopolistic, centralized, administered-by-shady-characters-who-like-to-work-outside-the-constraints-of-markets, unaccountable, political decisions will inevitably lead to unintended consequences, creating further disputes, distortions, force initiation, monopoly, centralization, and politics. And lawyers. The only remedy for this, short of abolishing the thing, will be for it to assume additional powers in an attempt to undo the consequences of its existing powers.
Unlucky thirteenth, numbers two through twelve add up to a growing, power-hungry, collective, misinformed, distortion creating, force initiating, political, administered-by-shady-characters-who-like-to-work-outside-the-constraints-of-markets, rule-by-fiat, monopolistic, unaccountable state.
Then even the flimsy defense of “but it’s volutarily funded” is out the window.