Take your pick. What do you want to see in terms of landscape? Most people suggest the inland road. Take chains. Check weather forecasts once you're there and if they predict snow then don't try & drive it. In winter I'd allow for a long day from CHC to Queenstown by road. As someone else said, take chains. Don't speed. Black ice will abound and it will kill you if you try to outdrive it.

Or, it could be a warm winter and simply raining or perfectly fine. Possibly all three on the same day.

Enjoy.