I have been in NZ a long time and i have moved around a bit. Although i do not claim to be an expert, i know this place pretty well..
Here is my take on it:
The North island:
Renowned for its beaches and warmer climate. It also has far less native forest and bush land compared with the south as almost all of it has been burnt off since European settlement.
Almost 3.5 million people reside in the North island, around 75% of New Zealand's total population.
Home to Auckland the "Supercity" - population almost 1.4 million and growing.
Home to Wellywood (Wellington), New Zealand's capital city, political center, film-making hot spot and soon to be second most populous urban area of New Zealand.
Much stronger Maori culture is found in the North island and also far more of the Maori population compared with the South island.
Far higher immigration count than the South island, mainly in the greater Auckland area.
Higher ethnic diversity, again mainly in the greater Auckland area.
More people, more jobs, more cars, more traffic, higher crime and depending where you buy, you will pay more for a decent house.
The South island ... the "Mainland":
Far more dramatic and eye catching scenery .. snow covered mountains, glaciers, fiords and varying climate throughout its own regions - best of all it still has large areas of native forest and bush land. Because of this tourism is a strong part of the South islands economy.
It is colder than the North island, but also is home to Nelson/Blenheim and its high sunshine per year count (they bounce back and forward).
The South Island has a smaller resident population of just over 1 million, around one quarter of the New Zealand population - it is also the largest land mass of New Zealand.
More than 90 percent of people in the South Island are said to be in the European ethnic group. It is also not as multi-ethnic as the north island.
Major center for electricity generation, producing over 40% of New Zealand's total electricity generation - this is mainly from Hydro-dams (95+%), but there are also wind farms.
Lower crime rates, cheaper housing, close to no traffic congestion. Some would argue an easier life style.
Home to Christchurch, the second biggest city in NZ, although that may change with ongoing earthquake exodus.
Queenstown - no further comment needed.
Penguin's, Kia's, Kiwi's etc etc still live here and can actually be found in the wild!
It is also common knowledge that South islanders are not as soft as North islanders