I've never actually been to Padding Markets in Sydney, so take this with a grain of salt, but probably the biggest/most-varied market in Melb is the Queen Victoria Market (or just "Vic Market"):
It's sort of split between food and "other stuff" - The fresh food (ie: meat, vegies, fish) are fantastic, but the actual food stalls generally leave a little bit to be desired (in my opinion).
The other alternative is South Melbourne market (http://www.southmelbournemarket.com.au/) which is not quite as big, but also quite good.
They both vary a bit depending on season (more fresh food in summer + night market, less in winter) but always worth checking out.
Be sure to check the sites for opening times as they're not open every day. about 10 years ago
Melbourne has a bunch of night markets which are closest to a paddington markets equivalent.
The Gaslight Markets are a good example (no link I could find, sorry), at the corner of Elizabeth and Victoria Street, but only on in the summer as far as I know... about 10 years ago
If it's clothes, and trash and treasure you're after (I also haven't been to Paddington, so this is a guess!) Camberwell market is great. It's on every Sunday. Lots of secondhand clothes, hand-made items, plants, books, antiques, records, random cool junk...
I think you'd be a bit disappointed with the Vic and South Melb markets if you were after anything other than food (but if it's food you want, Vic market's definitely the place to go!) about 10 years ago
Queen Victoria Markets is great for food but other than that it's pretty much the same as Paddy's in Sydney's Chinatown. Lots of rows of the same sort of thing.
Camberwell and Rose St are much closer to Paddington than QVM. More unique stalls with plenty of quirky and cool things scattered about. about 10 years ago