NY-NJ war had its origins in the constant tensions that Tony and his family were creating with NY in season 4 and 5 and then in season 6 it was Phil who somehow wanted a conflict. Unrealistic or not, it's not like the writters came up with this idea in the last 5 or 6 episodes.

Personally, I liked how they included a mob war in the series. I imagine this is how a modern mob war would look like. I'm glad that they didn't make some cheap hollywood spectacle with lots of shootings and bodies on the street (like in the 3rd season of Boardwalk Empire, where like 50 or more gangsters were killed in one night), just few high profile guys got whacked and there was quickly a stalemate. IMO it's a really good portrayal of a mob war and it's a nice way to finish the series.

NY family indeed had 200 made guys, but how many of those made guys were capable hitmen? We don't really know, most of them were probably old just like in the real 21st century American LCN. They certainly had more manpower but the Soprano family from the series was quite lethal - they commited many murders, had contacts in Italy and they had capable and proved hitmen like Walden, Benny etc. Besides, the NY family was in chaos, Phil took over after an internal war and his position was probably not yet solidified. I guess Tony and guys loyal to him had some hopes that their war with NY would spark another internal war in that family and they would end up with whoever would be against Phil and his administration. Also, the Sopranos basically had no choice but to defend themselves.