done it twice, first time trying to do most of nz in three weeks, fun BUT!!!!!
second time spent a week on north island just driving around.
Depends on what you want as to which is the better island, both have there own charms, north is far more populated than south. North is warmer. Coromandel is nice, as is the area south of Taupo, Rotorua, is interesting, if only for shopping in pak n save. If you want to see the thermal mud pools, you can pay and go to one of the "theme parks" or go to a park in town for free. the views in Kaikoura is IMO incredible, but I preferred the dolphins in the Bay of Islands to the whales? If you want to see Kauri trees then you have to go north, which means you loose time going south.
Basically you won't have enough time, to do half of what you would like. So think of what you want or just see what happens.
Word of warning do NOT UNDERESTIMATE THE SUN!!!!!!!!!!
first time I went out there I walked from where I was staying to mission bay, about 30mins each way. For the following three weeks my legs were weeping, skin peeling off! It was mid teens, late afternoon, cloudy and early January.