It's true that different countries have different banking security rules, but for Americans, credit cards definitely carry less risk. Our liability for credit card fraud maxs out at $50 as long as the issuer is informed within 2 business days; any false purchases or advances beyond that will be refunded, and there is no connection to our bank accounts from our credit cards. (Note that if you're going to add a teen as an authorized user, pick a Visa or Mastercard, not Amex or Discover.)
Personally, for overseas travel, I find that one card is not enough if you are traveling on an itinerary with frequent movement. If something happens and the card is lost, damaged, or compromised, the credit card company will normally take 2 business days to get the replacement card to you via a service like NHL or FedEx, and if you are moving from place to place on a motorcoach tour, that can be a difficult proposition. I normally carry two cards if at all possible. Also, I know cash is passe, but I get some immediately on the first day in a new country, because there are just sometimes situations where a card won't be accepted for whatever reason. (A couple of years ago I went into a butcher shop in Marylebone and bought a couple of links of sausage to make for breakfast in our temporary flat. The owner insisted on cash, as he didn't want to pay a merchant's fee on my very small purchase. He actually wouldn't change a 20GPB note, either; insisted that the largest thing he would take was a 10. And yes, I know he was probably breaking the credit card issuer's rules, but I really didn't want to make an issue of it; I just wanted 1/4 lb. of very nice sausage, so I handed over cash.)
Another place where card acceptance can be hit or miss is street markets; and tourist teens do tend to like to visit those, so getting a bit of cash for walking-around money is still not a bad idea.