I use my ING debit card only for overseas ATM withdrawals, and only where there will be a local bank fee charged.
Macquarie debit card for everything else as while Macquarie don't charge overseas transaction or withdrawal fees, they don't refund overseas operator fees.
I opened the ING account specifically for use at overseas ATMs. My last trip pre-fortress Australia was to Argentina, where as one of the other contributors mentioned ATM fees are extortionate and the amount you can withdraw is limited, if you can withdraw anything at all (it's largely a cash economy and ATMs regularly run out of money).
Some things to be aware of:
1. If you don't use your card for six months, ING will lock it. They won't however notify you of this, and there will be nothing in online banking to indicate it. You will have to call them to reactivate it.
2. When you do call them, they don't answer the phone. 22, 26 and 34 minutes was how long it took before I spoke to a human on my first three calls.
That said, Macquarie don't answer the phone either. None of the online banks do. I miss Westpac.
3. ING only refund fees on the first five ATM withdrawals. After that they slug you like it's 1997. So if you can, choose your withdrawals wisely e.g. in the UK and France there are no non-customer ATM fees, so no need to use the ING card there.
4. If you try to make an online transaction when overseas - like buying something from ebay or Amazon or leboncoin - you'll need a security code. The only way to get this is by SMS to an Australian mobile number. So if say you're using a local overseas SIM, like all good AFFers would if anywhere for more than a few days, then you are SOL. This regardless of whether you've notified ING that you are travelling overseas. Or given them an overseas contact number. Of course, nowhere do they tell you this, nor do the majority of their CSRs know it. As you can probably infer, this took a good few very frustrating hours of my time on last trip to learn.
There is no other option than SMS to an Australian mobile. No email option, no Authenticator app code.
Macquarie uses an Authenticator app. Doesn't matter what SIM card you have, it's tied to the device. You don't even need to have mobile service, as long as you have the device and are online.
5. ING's app is basic. It was good when they were the first online bank, but that's almost twenty years ago.
As far as exchange rate goes they're both as good as you'll get (outside of a specialist forex service like OFX, which requires an overseas bank account).
ING uses the standard Visa rate, Macquarie the standard Mastercard rate, which are both almost the same. Neither take a cut on top. Some days Visa may be slightly better, other days Mastercard, but the difference is negligible.
With either, always choose to be charged in the local currency, never use the offered local conversion rate at the ATM or EFTPOS machine. Same for Paypal or Amazon, they'll default to making you use their conversion rate, don't, use the card's. With Paypal this is very easy to miss.