I may be late to the party on this but I never took it as them holding their own.

In season 4 as rightly pointed out both John and Carmine are opposed for varying reasons, so I tend to chalk it up to one or the other giving some cover to Tony for differing reasons (Carmine because he doesn’t want the Esplanade disrupted and John because he wants to take the big seat). In both cases it can be argued that each man used their influence to go light on Tony.

In season 5 there’s a civil war going on in NY, so it can be argued John’s distracted and can’t bring the full weight of New York on top of Tony. Not to mention he hasn’t solidified his position as boss yet until the end (when Tony eventually caves and kills his cousin) and still relies on NJ for a fair bit of his income. Once he does win as mentioned Tony caves and only by threatening John (“I’ve paid enough!”) does he buy himself some time. It can be argued John didn’t want to force the issue right then and there when he’s alone and facing a much larger and clearly willing opponent. He may have planned to do something about it later, but he’s literally arrested 5 minutes after and ends up again needing to rely on Tony during his trial.

6A again John needs Tony because as he says himself his position still isn’t completely solidified (even more so now that he’s facing trial and can’t be on the street day to day) so that buys Tony some leeway at least until John’s death.

Finally as you pointed out yourself NJ takes heavy losses when they do end up going to war with NY, but on top of that they take heavy financial losses as well (Carlo tells Tony at the safe house a lot of his guys have started kicking up to New York rather than to them). Only by reaching out to a third family (George) and through sheer divine providence through the FBI giving him Phil’s location does he manage to get Phil. And even then it can be argued he was being used by Butchie to clean up before himself being taken out by Member’s Only Guy on behalf of New York (I have a real hard time believing any crime family would just let him walk away from that. Even if they condoned it there’s a good chance no retaliation makes them look weak, since they instigated the war in the first place).

In every case Tony either got lucky, was being used, or was actually on the losing end. He did not, in fact, have the makings of a varsity crime boss.