In the American system- mediation is exclusively within the control of the two parties. The mediator (or mediators) is nothing but a go between, a facilitator, a neutral, party. Mediation is non-binding, though any settlement reached is still a settlement.

Arbitration is like a pseudo court/trial. One arbitrator (or three..usually odd numbered) is given exclusive control over the proceedings. You present evidence (though very relaxed in standard) to the arbitrator(s), and a decision is rendered. It can be binding or non-binding.

PT- sounds like you had a bad experience with arbitration, as in mediation (at least in the US) if it wasn't an issue to either party, it wouldn't be an issue to a mediator. Their job is to facilitate, not 'rule'.

I think both have HUGE benefits- one of which is the cost of legal representation at a ARB/Med vs. a trial, is usually way less. I encourage any one that comes to me to look at that as a possibility. Many people simply (and stupidly) don't want to do that. They have seen too much Judge Judy and the like to think that court is 'better'. It is rarely 'better'.