At this point two things happen. First, the stance of the parties becomes adversarial and competitive. The goal in the legal system is to have your side win as opposed to finding the best solution. Secondly, control of the process leaves the hands of the disputants themselves and enters the hands of the experts - lawyers and judges trained in principles of law but not in human communication. Arbitration and adjudication are both legal processes involving win-lose paradigms.
Arbitration is a less formal and more gentle process, as well as usually much quicker.
The rules of evidence in arbitration are far more relaxed and less stylized than in a judicial proceeding, and arbitration is usually voluntary whereas trial proceedings are not. Nuclear war is the most extreme example of this kind of lose-lose method of dispute resolution. Because the parties talk until they reach a solution, it often produces a workable, satisfying result in a way not possible from an adjudicated decision. The process of mediation is cheaper, quicker, and in many cases fairer than the average lawsuit. Perhaps more importantly, mediation builds community because it encourages conversation between the parties and upholds their ongoing relationship.