I just used my BB card at a Westpac ATM in Sydney, Australia. The ATM charges a AU$2.00 fee (in addition to the US$2.00 fee charged by BB). The exchange rate was the best market rate that day.
In contrast, I also used my SunTrust Debit MasterCard at the same ATM. This time the ATM charged NO fee (and neither does my bank for the type of checking account I have). But SunTrust adds a 3% surcharge to the best market rate, so the net result was nearly identical. I ended up using my SunTrust Debit MasterCard for the remainder of my ATM withdrawals.
I checked the ATM fees in Sydney at several banks. All charge a AU$2.00 fee for BB withdrawals. All (except Westpac) charge a AU$2.00 fee for SunTrust Debit MC withdrawals. Westpac has agreements with several foreign banks to not charge a fee for ATM card withdrawals using the foreign bank's debit card. Apparently, SunTrust must be one of them (although it's not on the list posted at the ATM).