I know that NJ had its own families, like the DeCavalcante in Newark, but did they or others become as powerful and pervasive as, say, the Gambinos or Genovese were across the Hudson? Or was it more like what Phil Leotardo described in The Sopranos: "Five families, and then we got this pygmy thing over in Jersey".
A question that takes me back to my homeland, the Garden State!
In general, the perception given in The Sopranos is more-or-less correct, as New Jersey organized crime families tend to be upstaged by their brethren across the Hudson River in New York City. While the DeCavalcante family, which OP mentioned, was a force to be reckoned with inside New Jersey, Mafia Encyclopedia author Carl Sifakis concludes that the family’s leader, Sam “The Plumber” DeCavalcante, was “hardly an important Mafia godfather,” and acted as “a sort of gofer for the commission in its efforts to tame [Joe Bananas] Bonanno.”
In many ways organized crime influence in New Jersey reflected the bigger social and economic divisions of the state. North Jersey was in the shadow of Gotham, while South Jersey—particularly Atlantic City—was dominated by Philadelphia organized crime. In the 1980s, mob warfare in Philadelphia that claimed several lives, including two successive leaders, Angelo Bruno and Phil “Chicken Man” Testa, centered on control of Atlantic City rackets. That this bloodshed involved a struggle between New York and Philadelphia mobsters rather than indigenous New Jersey Mafiosi speaks to the position of New Jersey mobsters at the time.
Bruce Springsteen chronicled the influence of the Philadelphia mob in "Atlantic City" (1982): https://www.youtube.com/watch?v=M3eu1gW-bQ8&feature=share