Hobart wins if you want MONA, the waterfront, and easy access to Bruny Island and the Tasman Peninsula. Launceston suits travellers focused on the north — Tamar Valley wine, Cataract Gorge, and a shorter hop toward Cradle Mountain.
Many visitors do both on a longer Tasmania trip. If you only have a few nights, choose the city that sits closest to the regions you care about most and day-trip from there.