Culinary Capital of Aus - Syndey or Melbourne?
That's easy - both. And that is a serious answer, the question like asking if red or white wine is better.
IMO Melbourne does great mid priced restaurants, lots of quality and great cooking at keen prices. Places that are atmospheric with lots of style. Sydney probably has the edge at the top end with some very heavy hitting fine diners, great for really glam nights out, with exceptionally fine cooking. Sydney also probably does Asian better, with more cross over.
But both cities will have many exceptions to this crude division but great restaurants at every price point and style. Bottom line is I think they complement each other really well.