Personally, and I do appreciate everyone's different here, I would sort it out myself. Do plenty of research - and there are good sites out there, this one for example, Lonely Planet's Thorn Tree forum - and use the money saved to good use, extra activities, nice hotel here and there.
Oz and NZ are relatively easy to travel to and around on your own steam, no language barriers. Like I say, research loads, ask as many questions as you need to on these sites and you should be fine. The Kiwis in particular are such nice people that any problems you do have, they will be more than happy to help you with.
Doing it this way, would give you more sense of freedom to do what you want, when you want and give you the opportunity to go off on a whim, should you see / find something different / not on the agenda that you want to do. Plus, it gives you more flexibility on choice of hotel / accommodation...eg. nice little cottages in middle of nowehere in NZ.....poss preferable to being 'herded' about to 3* / 4* hotels in a large group.
That's my opinion anyway. Good luck with whatever you choose. They're both great places.