My first time overseas, I had to exchange money in $200 of travelers checks to pay a mountaineering guide who hadn't heard of American Express. The bank charged me $8. During the same trip, I used my debit card at an ATM to get $200 from my checking account. two times home, I saw that the charge for this was two dollar, and that was the last time I used traveler's checks.
When an Automated Teller Machine (ATM) won't take two of the cards for some reason - and this will happen - I use the other card, which usually works fine. Credit cards may be less trouble than debit cards. Your liability could be zero on your stolen debit card, but you probably won't have access to your account until the matter is sorted out.
I usually carryover a debit card and a credit card when I travel now. I keep them well-hidden in two separate places. If they are stolen, which has never happened yet, they've either zero liability, or a fifty dollar liability limit for any unauthorized charges. Ask your bank or credit card company about this.
Of work, on longer trips it is a hassle to pay the credit card bill on time, which is not a problem with debit cards. carryover both, and on longer trips you can wait until you are a few weeks from home to use the credit card. That way you'll get there before the bill does.
An important advantage credit and debit cards have over travelers checks, is that when you need the local money, you'll almost always get a better exchange rate with your cards. Also, the money you get from the local ATM will truly be accepted everywhere, something even American Express Travelers Checks cannot promise.
i have nothing against American Express. two times, when I was robbed in Mexico, they quickly and curtiously replaced my stolen traveler's checks. Also, at times it is appropriate to carryover money in several forms, including theirs. However, times alter and ATMs are everywhere now, so my policyowner is : Travelers checks; don't leave home with them. You can take an American Express credit card instead.