3 days is certainly very tight. For both Tas and NZ South Island, the major draw is getting out into the great outdoors. If you just want to see the scenery, then NZ around Queenstown is probably 'better' since some of the deep glacial valleys and tall mountains are viewable from the main roads.

If you do 3 days in Tas, I would suggest flying in to Launceston, see Cradle Mountain and Dove Lake, then either follow the east coast (Bicheno, Hazards at Freycinet) or west coast (via Strahan and Mt Field) to fly out of Hobart. If you stay around Hobart, take a day out to Gordon Dam. If you want to see the wildlife, stay at an accommodation out of town that has native bushland.

For Doubtful / Milford Sound, low cloud can mean the sightseeing flights are cancelled quite often, which makes planning for 3 days difficult. If you head that way, consider splitting your stay between Queenstown and Te Anau.