If an inspector is suspicious that you may be trying to use a Eurail pass when you are a European resident he may ask for some credible proof that you are residents of a non-European country. As long as what you show is a credible ID document he will not compare it with a list of “acceptable” documents. 

As ever this is one of those open-ended guidance/rules but any sensible inspector would accept something in your name with an official or credible identity such as a driving licence, ideally with your home address on it. If you have a second ID just in case that should seal it for the most suspicious inspector.

There is only one operational difference between the 2 passes which is the Interrail global pass that you can only use it in your country of residence for a maximum of 2 days, so you are only likely to be seriously challenged if you seem as if you are in the country of your citizenship - As a Yorkie it is fairly obvious as soon as I talk that I am probably a Brit.

If you have an obvious Australian accent and an Australian ID document you will be fine.

Why don't you use your Australian passports for your Eurail pass? You can still use your EU passport for border crossing. 

A driver's licence is not a valid proof of residency. I have asked the question to Eurail Customer Support and here's the answer:

"Dear Anna, 
 
Thank you for your message. 
 
Please note that a driver's license or an e-residency document is not a valid travel document.
Please check the following page for more information: https://www.interrail.eu/en/support/interested-in-interrailing/do-i-need-an-interrail-or-eurail-pass
 
Thank you and have a nice day! 

Best regards,

Mansur
Customer service team"

Lots of people are resident in countries without having passports from that country.

Eurail simply refuse to acknowledge this reality as well as ignoring the fact that the majority of countries do not issue ID cards to residents.

The travellers state in their question that they are Australian citizens, thus they would probably have Australian passports to facilitate the travel back to Australia.