Seat/pitch rules out NZ in Y. It's cramped and uncomfortable.
QF and FJ are about the same on carry on in terms of whether they police it. Just don't be the cliche American and try to bring on a 22 inch case packed to the brim and you'll be fine. Remember, weight limits are less than the usual US 10kg limit for carry on.
Price will be whatever it is when you look & buy. No one can predict that one for you.

That said, I've flown all three. I actively avoid flying NZ if I can. I don't have a great love for QF but they tend to get the job done. Their A380 is quite tolerable in Y if you pick the right seat. I'm somewhat of a fan of FJ, but I've haven't flown Y with them since they had the 747's so can't really comment on what it's like at the back end. The front end post-747's have all been nicer than QF or NZ IMO, and that includes having flown QF F on the A380 - that was an absolute shambles of a flight.