NYC civil (divorce courts) use one-- in most cases, divorces are purely a civil matter, but sometimes (rarely) an orthodox jewish couple will divorce. most of the time, the divorce and settlement will be worked out by a court of rabbi's, and their settlement, is often taken by NY courts as 'fair and equitable' --often there are complicated terms, and financial settlements that don't quite meet the NY code (which has a formula for child support, and since NY is a community property state, each spouse is supposed to file financial records, and the court get to go over them, and insure there has been equitable distributions of assets.)
rabbinacal court use in effect, a 'jewish common law' based on the talmud law and custom, not english common law... but the NY courts will very often accept in toto, their 'decisions'.
Jewish women are only considered divorced if they have a "GET" (might be spelled differently, i only know it as a spoken word)--and their husband has to provide it. (he can remarry with out a GET, but she can't.) You might think this makes them vunerable. (the rabbi's do!) so rabbinical court (and thousand of years of talmudic law) tend to look out for the wife and children. a study done in the 1970's (a long time ago) compared divorce settlements, and orthodox settlements tended to be better at protecting the kids, (at the expence of the wife) slightly more than civil courts settlements. but, in general they were about the same.
orthodox couple can complete skip the rabbical court, and get completely civil divorces, but divorce is rare, and civil divorce (with out a religious/GET divorce) is very rare.