How are sharia courts different from "rent-a-judge"?

I have no particular interest in this subject -- the only reason why I am posting this is that some stupid troll, in response to my article about some anti-Darwinist statements made by the Archbishop of Canterbury, made an ad hominem attack on the archbishop -- calling him a "bedwetter" and a "wuss" -- based on some statements that the archbishop made about enforcing decisions of sharia courts in the UK.

As pointed out by this article, the decisions of sharia courts are now enforceable in the UK only if both parties agree to arbitration by these courts. How is this fundamentally different from the "rent-a-judge" practice in the USA? In the USA, parties in a dispute who want to bypass the slow government courts -- which can take years to reach a decision -- can agree to "rent" retired judges at rates of up to several hundred dollars per hour. How can these "rent-a-judge" agreements work if the judges' decisions are not accepted as enforceable?

Also, Eugene Volokh of the Volokh Conspiracy blog posted an article generally supporting the archbishop's statements about sharia courts. Anyway, even if one does not agree with the archbishop, his statements are hardly outrageous.

"I'm always kicking their butts -- that's why they don't like me."
-- Gov. Arnold Schwarzenegger