There is one power a judge holds that an arbitrator does not: the contempt power. However, litigants are rarely held in contempt of court and when they are, the sanction exacted most frequently is not jail but some impact on outcome in the case. Arbitrators, too, have the power to impose this kind of punishment.
In light of the extraordinary discretion given to an arbitrator, the selection of an arbitrator is a critically important task. With limited exceptions, litigants have no choice in the judge before whom their case will be litigated. But processes established by the rules of arbitration services do allow for considerable choice, subject to the limitation that there is an adverse party that may exclude arbitrators who are attractive to you.