Be prepared for some opinions to be presented, MEL and SYD have quite a rivalry.
First the 'pros' for Sydney. Sydney has more 'wow' factor IMO, the harbour is quite the iconic Australian sight. Sydney has better intra-city beaches. You can take nice ferry rides. You can take a train from the airport to the city.
Melbourne has a better restaurant scene, no doubt. It's a more interesting city to get to know, lots of hidden gems and surprises. Better coffee. It's a nice city just to be in. I think Melbourne is 'prettier' than Sydney on average, with loads of parks, etc. But it doesn't have a major attraction that is the equivalent of Sydney Harbour.
Outside the city, Melbourne has Phillip Island, the GOR, Yarra Valley, and the Australian Alps. Sydney has Hunter Valley and the Blue Mountains. Respectively, I think Melbourne wins here.