Having visited both, I'd also go for Cairns over Auckland, though you might want to consider actually staying in Port Douglas as opposed to Cairns.

All the major dive companies operate out of Port Douglas, its a slightly shorter trip out to the reefs and the resort areas in Port Douglas are, IMO, much nicer than Cairns. The 4 mile beach is wonderful for an evening stroll, and there is a lot to do in the local area on your last day if you are looking for land activities after diving. I was last there in 2005, i spent a few days out on the reefs and spent the last day touring Kuranda and the rainforest before my flight to AKL.

I've used Haba Dive and Quicksilver for my trips. I thought there were just too many people on Quicksilver, Haba were much more personable. I'd agree with flyingzzzd's on the Cod Hole diving. Seeing Potato Cod for real and close up was absolutely amazing!