This is a simple choice:
Melbourne has the International Comedy Festival, the Arts Centre, the Formula One Grand Prix, the Australian Open tennis, the AFL Grand Final, the Melbourne Cup horse race, the Boxing Day Test match and stunning botanical gardens everywhere. In fact, almost everything that happens in Australia, happens in Melbourne.
Sydney is also 50% more expensive than Melbourne.
The only real question is whereabouts in Melbourne you should live. Do you go for somewhere near the water (such as Williamstown or St Kilda), somewhere central (such as Jolimont or the Docklands) or somewhere nice for families (such as Montmorency or Macleod).
You can get your Sydney fix once a year for a long weekend, because Sydney is an excellent place to visit, but not the greatest spot to live.