Both are great cities. I like them both. But each is very different.
Melbourne (Victoria) is cold, wet and miserable but is the Mecca of sporting events. It is AFL (Aussie rules) country but rugby is getting more popular. Public transport is excellent (trams and trains). Best coffee baristas in the world. Hard to find a bad coffee. Also good eating strips! very multicultural. But it has DickieE!
Brisbane (Queensland) is hot and humid ( and too far from the beach if you ask me) so during summer months you're always wet and sticky as soon as you leave the comfort of air con. Oh - it also floods there a lot! It has the worst coffee in the world - it's hard to find a good one! It is league country and their whole existence is about winning state of origin. That is more important to them than good govt services! Pity it is plagued with queenslanders! They finish every sentence with "ay". Union plays 2nd fiddle to league. Great beaches north (sunshine coast) and south (gold coast).
Both cities are pretty safe, although they have their pockets of trouble spots. Either city is great, but if it was me I'd go to Brisbane.....but I love the sun and sea and am sick of the cold!