I live in Melbourne and have visited Sydney recently and I must say, Sydney must seriously be on drugs if they can compare themselves to us.
Firstly, the roads are shit.
Who the hell has a city centre with so many one way streets that a trip around the melbourne CBD could take 2 minutes whereas Sydney, a trip of identical distance could take up to 20 minutes because of all the dumb one way streets?
Secondly, Melbourne has a much much larger community that supports sport.
Hell, if we had all the Australia Socceroos games, we would fill the MCG EVERY TIME AND STILL not have enough space to seat everyone who wants to go.
Thirdly, everyone in Sydney looks like they want to commit suicide and always walks around with a phone against their ears.
Come down to Melbourne and you will see what a proper friendly city is about.
Fourthly, the city itself is overrated. The only place that gets remotely close to Melbourne's greatness is Darling Harbour. Note my emphasis on the word remotely...
Fifthly, we have the Australian Open. You cannot take that away from us as we have far better facilities and again, we FILL the tennis centre. My proof you can't have the Open? You have the Medibank International and yet you still can't pull crowds like we do.
Sixthly, don't call yourselves 'very multicultural'. The only multi culture you have up there is Chinese, Vietnamese, Indian and the RARE Greek and Italian. Far out, I couldn't find a bloody Italian restaurant, not a pizza joint. Here in Melbourne, we have EVERYONE and when I say everyone, I mean it.
If I wanted to, I could visit a different restaurant of different cuisine for every single night over 2-3 weeks AND we have Australia's first pizza restaurant, Toto's, in Lygon Street. However in Sydney, I would be stuck with noodles, sushi and curry.
Seventhly, everyone is too casual when it comes to work days. Out of all the office workers I saw in the CBD, only 20% were dressed appropriately in suit and tie. Here in Melbourne, suit and tie is expected dress code for office workers, regardless of being in the contact centre, IT departments, Sales departments, etc.

So come on, I challenge you people from Sydney on this website to read this and to try and think of ANYTHING that you do better than us and I can guarantee that we have anything better... But you can keep the Mardi Gras... we don't want it thanks.
As for history lessons go, I recall that we have Captain Cook's cottage in our gardens here and we have the first parliament house on display at the east end of Collins Street...