Adelaide has a fantastic climate, can get too hot during those heat waves though! It is certainly different to Melbourne, completely different feel to the place.
We live in Adelaide, the southern suburbs (20 minutes drive from the CBD) and enjoy the quiet slower pace here, there is plenty to do, people are friendly but finding employment a couple of years ago was difficult as we have found it a place that employs the "its not what you know but who you know" rule (very clique).
We visit friends in Melbourne a couple of times each year and love the hustle and bustle that Melbourne offers, it has a vibrant feel and the city centre with its pavement and back street cafes make it very appealing. However if your living in the suburbs I imagine its pretty much the same as anywhere else although it will be a lot more expensive than Adelaide, roads are busier and most likely your commute will be longer too.
You need to ask yourself what you want, we would not move to Melbourne from Adelaide as we feel we can have the best of both, just over an hour away on a flight and you can usually pick up a bargain, but having said that I think we would be very happy if we did live in Melbourne. (Would we visit Adelaide if we lived in Melbourne...probably not)