For me, there is only one possible answer here. That is that In re Gault is the case that has had the greatest impact on the juvenile justice system. The reason that this case has had such an impact is because it has made the juvenile justice system more formalized and similar to the adult system.
Before In re Gault, the juvenile justice system was informal. Juveniles essentially had no right to a lawyer and not right to any particular due process. Juvenile proceedings were like a parent just sort of deciding what was right for their kid based on whatever they happened to think best.
After Gault, that all changed. This case mandated that juveniles receive most of the same due process protections as adults. It ordered that they be provided with lawyers. Basically, for better or for worse, it made juvenile courts into a version of adult courts with a very adversarial and formalized process.