Campervan vs Tent Camping through New Zealand

Our original plan was to rent a campervan a little larger than the one we have now in Australia for our tour across New Zealand, but are beginning to rethink that strategy.  We've come across quite a lot of places in Australia that are only 4-wheel drive accessible or only allow tents overnight, especially in the National Forests.  Since quite a bit of the South island is National Park land, we're concerned we may miss a lot of opportunities in a campervan.

We need advice from anyone who has traveled through New Zealand either by caravan/campervan or by tent on what you think the better approach will be.  We'd especially love to hear from the Kiwi's we've met along the way so far.   Thanks in advance!