There is a big difference between a Transatlantic and anything really. But like you I prefer NY-NY and have done both several times.
Passengers, same mix of Yanks and Brits with a scattering of others. Entertainment, same. Enrichment programs same, depends on who they pick up but you may get Cunard or Titanic speaker on Transatlantic.
Fencing, yes. Tea on port days, umm don't think so on Mary but my be wrong.
Overall, for me the ship is the destination. When in the Caribbean I rarely bother to get off. You will have largely the same onboard experience on either itinerary so usually price determines which I choose.