3 days is enough to see Queenstown or Hobart, with maybe a quick daytrip to another spot. It is not enough, as others have said, to explore the South Island or Tasmania in much depth.

Queenstown is more spectacular than Hobart. The south island has more to offer than Tasmania (in my opinion). So the easy answer is Queenstown, but if you had 3 days this trip and the potential for 7 days later, I'd be inclined to spend the 3 days in Tassie and save NZ for a longer trip.