I mentioned this point in my previous posts " Only Piss poor in ICC knockouts". In this department, Australia got an immense edge over India.
But in Test format, they are slightly lagging. One main parameter to judge is to just look at how both of these teams perform in each other's territories. The last time Australia won test series in India was way back in 2003-04 and India has won 2 series in Australia.
Don't judge Australia performance when they are up against low ranking teams like Pakistan or Windies, especially when they are playing at home. One can make an argument for an away series though, even against low ranking teams because most of the teams are largely dominating at home.
We can't justify anything here with our stats and calculation because main thing is who is winning and who is taking silverware with currently Australia is leading country, and they are doing impressive work with their quality and consistency even there is no doubt India is also good side with their recent results in all formats but still they are choking which is fact, and they need to overcome these weak points if they also want to have any mark around the cricketing world.
Australia is winning against weaker sides so can you justify South Africa is strong side or Afghanistan is strong side as all are having same level teams and same level conditions, but Australia is good and aggressive with they are also having best cricketing system which is producing the best players which are giving their best in all conditions.