I was born in Motueka, my wife in Middlemarch, so we are expat South Islanders. We lived in Auckland for seven years after we left Dunedin, and now live in Wellington. Moving to Wellington was a compromise between available work, and being close to our families (and the mighty South Island!). My take on the cities I've lived in:
Auckland: Best cultural diversity in the country (good thing). Most things going on of any city. Entertainment always available. Central City rat race can be very tiring and ultimately soul destroying. Sooo much travelling to get anywhere. West, South, and East Auckland are all great. North Shore is what gives Auckland it's stereotype*. Muggy!
Wellington: Home to the best local music of the last decade*. Cheap and speedy access to the South Island. Much more laid back and community orientated than Auckland. The weather is ... alright.
Nelson: Best region in the country hands down* - haha
Christchurch: Looks pretty. You get Akaroa. Good weather, but the North Westerly is a shocker. In the early to mid nineties this city was easily the most racist, conservative, and physically violent city in the whole country*. No idea about now.
Dunedin: Total playground for students, in a good way. Living there gives you Wanaka, Te Anau, Catlins and Central Otago on your doorstep. A New Zealand city with tangible heritage (Maori, Chinese, and European). Gets damn cold, but is often really still - so Wellington on a windy day can feel way colder. Surprisingly hot in the Summer, but not Alex hot.
Oh, and South Island roads are infinitely more fun to drive on than North Island roads*. That on its own makes the South Island better =P
*IMHO