Well DH and I are snuggly back in our cabins by 9 - 9:30 so I cannot at all speak on nightlife. (Though you'll see us walking the decks at 6:00am so I can give guidance on that 🤩).
I do not think that MSC has sailed out of New York before (though I could be wrong) but I would imagine that there will be a lot of local tri-state folks on the cruise which would infuse a certain New York ambiance. (Whether it's Upper East side or Bridge & Tunnel is another story...)
To me, Yacht Club on MSC > a balcony on NCL. But that's my personal opinion as we really enjoy staying in the bubble of the YC.