That is the question. The answer is simple. You would be stark raving bonkers to not visit both. For sure the magnitude and majesty of grand peaks lie in the South but the coastline and hidden bays are found in the North. Skiing is in both islands though Queenstown is the mecca for the snow followers.
One of the greatest drives in the world is the Pacific Coast Highway in the North island and is worth every minute. But driving the southern tip of South Island is empty, great for motorbike tours.
Rugby is everywhere so take your pick. There are great golf courses, the North Island being home to the incredible Kauri Cliffs Golf Club. Bloomin pricey but boy oh boy what a course.
The North island just pips it when it comes to wine regions with 6 of the 10 main areas.
But if you are visiting then truly madly deeply you have to afford the time and travel the length and breadth of this stunning, beautiful, adjectives galore country.

