If you do end up busing it and ferrying it from Auckland that really isn't a bad thing. The bus ride really is gorgeous.
Looking through various trail descriptions and pictures around SP, it seems that the most interesting area is the South Alps
If you have time, both are enjoyable. The South Island has the most rugged mountains (among the most spectacular I have seen anywhere on earth), but the North Island has things the South does not, such as active volcanoes, geysers and the Polynesian culture. If you have time, visit both islands. If not the South is a great choice.
We only had a month to see both islands and it was no where near enough time. Someday we'll be back.