Most sites say the north is warmer than the south island with more snow in the south.
And that is correct, there is very little snow on the north island,mountain tops only usually.
I have traveled over a fair bit of the north island and it is excellent country for riding in, the south island has more mountain roads than the north , i would love to tour round either island on a bike. My preference would be the north island as its warmer {spoiled Aussie here..
}. I can't speak for the south but the roads in the North island are pretty good, roads are well marked and in far better condition than Aussie country roads. I really enjoy my holidays in NZ and try and go every couple of years, my wifes family live in the centre of the north island in the lakes district and there is plenty of good countryside to ride or drive through there.
Mick