NZ wins premium economy and economy hands down.

Business, not a lot between them to be honest. As already mentioned NZ biz isn't great for couples due to herringbone config, although you can dine opposite each other. Not a big deal if you're not bothered about sitting next to each other though. The NZ cabin ambience / mood lighting is IMO a lot nicer than it is on BA. They both offer a relatively new cabin and fully flat beds and thus will both be pretty good.

This sort of trip in business class could net you Silver status on BA, or some sort of Star Alliance Gold card, if you played it right. Whether this is important to you or not I don't know, but if you like the idea of coming back from this one trip with shiny cards, people will be able to advise you of the best way to do it