I'm quite obsessed with this; I have even made a list for my spouse on when to use different cards (card purchases in SEK, ATM in EUR countries, card purchases in USD, etc...)
My rules when my wallet pays for things are rather simple: Cash is always better than points, so I pay with SAS cards or other Swedish miles/points cards only in Sweden, with the only exception being airline tickets in other currencies if I want to have Amex insurance. Otherwise I use a local card or a card with 0% exchange surcharge.
So my answer to your question in
nothing! But I am sure a lot of people have a different opinion.