With its internationally-renowned laneways full of street art, one of the globe's most highly-concentrated music scenes and world-beating arts institutions, many Melburnians consider their city one of the greatest cultural destinations on earth.

But to many people overseas, Sydney – with the white sails of its opera house an instantly recognisable international landmark – is the first Australian city that comes to mind when they think of creative capitals.

A Boston Consulting Group study commissioned by the Victorian government says a lack of promotion for the state's arts and cultural offerings and a failure to provide an overarching cultural guide for tourists is holding back cultural tourism to the state.

And we had better watch our back, it warns. "Melbourne's position as Australia's cultural and creative capital is being challenged," the report says, noting the NSW government's $600 million cultural fund (which just funded a new $244 millon Sydney Modern contemporary museum) as a real threat to our reputation as the cultural capital.

The National Gallery of Victoria, by far the most-attended public gallery in Australia, has spent several years fundraising for its equivalent, NGA Contemporary, without identifying a site or attracting government funding. 

According to the BCG study, cultural tourism and creative industries contributed around $23 billion to the state economy in 2015. 

While Australians think Melbourne is the most creative Asia Pacific city, according to a Global Traveller survey, our international visitors think Sydney is the most creative. 

But they change their tune once they visit Melbourne, the survey found, at least slightly, being 25 per cent more likely to recommend this city as a cultural destination. 

Melbourne's street art was among the biggest drawcards for domestic and international tourists, after Melbourne Museum and the NGV. The museum's 2011 Tutankhamun exhibition holds the record for highest attendance, attracting 796,000 visitors, followed by the NGV's Melbourne Now showcase of local contemporary artists in 2014, which drew 753,071 people. 

Melbourne's cultural offerings are not "cutting through", according to heads of institutions and influential arts identities surveyed by BCG. 

But the competition for cultural tourism has moved beyond the traditional Melbourne/Sydney rivalry, says state Creative Industries Minister Martin Foley. Now we're competing with Singapore, Seoul and Mumbai. 

Some of the research, such as international visitors' perceptions of Sydney as Australia's cultural capital, were a surprise, he said.

"We expected to outrank Sydney, but international visitors see it as the place to come to. But once they've been here, they see Melbourne as a cultural space."

Compared to Sydney, and other Asia Pacific cultural centres, Melbourne had a much broader, deeper creative offering and infrastructure, Mr Foley said. 

"As important as it, and I'm not playing it down, we're talking the whole ecology, including the small to medium companies.

"I wish [Sydney] every success ... I'm sure it will be good but in terms of square metre space, they don't come to the size of the two sites at the NGV.

"It's not about size, it's about reasons to give a wider demographic engagement.

"Everything from big cultural festivals to small things in between lifts us to that global vision of a 24-hour city and state."