An Australian version of the ship, built by the Spanish firm Navantia, is one of two competing designs for the $6 billion air warfare destroyer program.
The other is by US - based firm Gibbs & Cox, which is being developed by the 50 people working at its Adelaide office.
Three destroyers will be built at Outer-Harbor based ASC, which won the construction contract in 2005. Federal Cabinet is expected to decide the winning design in July and construction will start in 2009.
The Navantia design is thought to be the favourite because it is reportedly at least $500 million cheaper, would require a smaller crew and could be delivered two years earlier.
The Gibbs & Cox design would inject an extra $1 billion into Australian industry, while its rival would benefit Spanish industry.
A visiting Spanish frigate competing to be Australia's next air warfare destroyer was yesterday dubbed "a great ship" by a key federal minister who will help make the $7 billion decision in July.
The Government will choose between the Spanish F100 design, of which Alvaro De Bazan is an example, and an as-yet-unbuilt warship being designed by US company Gibbs and Cox.
The "evolved design" will be a larger ship, based on the US navy's Arleigh Burke-class guided missile destroyer, which is 155m long and weighs more than 9000 tonnes.
As an untested warship, the evolved design is thought to carry higher risks of budget and equipment problems.
Yesterday, Senator Minchin said he appreciated the opportunity to board the ship. "It is a great opportunity to see one of the two possible designs in the flesh," he said.
"As one of the decision-makers, I'm personally pleased to see this vessel in real life."
Since the Alvaro De Bazan was commissioned in 2002, Spain's navy has added another three F100 frigates to its fleet.
Built by Spanish shipbuilders Navantia, the F100 has long been regarded as a stalking horse for the Gibbs & Cox option.
But with $7 billion at stake, an Australianised F100 is now thought to be an even-money bet to win the contract.
Senator Minchin said "value for money will be a primary consideration in that choice" along with capability.
The Alvaro De Bazan and its crew of 200 men and women, including 20 heavily armed marines, will stay in Adelaide until Saturday. The ship will visit Sydney from next Monday for a week and will arrive back in Spain on May 19.
Update 11 March
Patrick Walters in The Weekend Australian sheds more light on the history of Spanish naval contacts with Australia. He says that the visit to Australia by the Alvaro de Bazan is the first by a Spanish warship since 1859. The rest of the article is also worth reading not least for Mr Walters' advocacy of the claims of the Spanish (publicly owned) shipbuilding firm Navantia and for his admission that his recent trip to Spain was paid for by Navantia.
Further Update 14 March
Yesterday's Australian had a full page ad about the "Armada" which was paid for by the Spanish government.