John Sacrimoni was more powerful than Tony until he was locked up and died. Tony was definitely powerful in Northern New Jersey in Newark and other surrounding areas once he became street boss and boss. His crews are formidable when earning and a couple are great earners, we really never learn what the other families were into, but for the time period the show was on, it would be whoever had a hold on Atlantic City, the unions, gambling, loansharking, Trenton, Camden, and southern New Jersey, will have more power than Tony. Many factors and not much information, that is why for Northern New Jersey I say Tony is powerful.
Pussy and his FBI handler talk about Phily making moves on Tony's turf so if Phily's moving in on rackets in North Jersey you know they control South Jersey, Trenton, Camden, AC, et al.
We have to remember however that David Chase said The Sopranos are mostly based on the Boiardo crew. That's Westside. That would also explain Tony not taking shit from the Lupertazzis.
Like with all fiction however I think The Sopranos are a composite of a lot of different mob families. Part DeCavalcante (especially in season 1), part Jersey Genovese, Part Jersey Lucchese. There's bits and pieces of all of them in The Sopranos storylines.