We have flown both F and J with NZ, long haul flights between LAX and AKL, two round trips in total.
On all four segments the crew went above and beyond to ensure we were as comfortable as possible, made sure we had everything we needed. They supplied bottles, diapers etc. Stuff we had already, but nonetheless wanted us to know they had extras.
The NZ bassinets are larger than AC's. Our baby did not fit AC's bassinet during the YVR-LAX, but easily fit the NZ bassinet LAX-AKL.
NZ will have you hold child (less than 2) on your lap for take off and landing, with a seat belt threaded through yours and around them.