Having used both fairly extensively, I'll go with Melbourne.
Sydney's point-to-point ticketing system sucks. The prices of tickets suck. The fact that the fastest way to get most places 1km away in the CBD is to walk, sucks.
Sydney might have better coverage to Melbourne out in the suburbs, and certainly have better busses out there. But again the ticketing shenanigans negates a lot of this. Unless you have a periodical ticket (weekly/monthly), there is no flexibility. You paid a fair to North Ryde? You're going to North Ryde. You can't change your mind. You can't decide to hop off at Woolies on the way home and get back on. Your ticket is valid for just the journey you initially paid for. Did I mention it sucks?
There's good things about Sydney. The trains and ferries are better than Melbourne's. It's just the network is so damn unfriendly and expensive to use. Yes it sucks that you can't always just buy a cash ticket on Melbourne's network. But getting set up with Myki takes no time.
It sure is nice to hop on a train to Sydney Airport, though. Pity it costs $25 or something to do it.