I'm sorry, I've never used the traveler cheque card. I never leave home without my traveler cheques however. I prefer them, because for me it is easier to budget my money. Each night I can count how much I have, & what I spent. I'm surmising with the card I would have to remember how much was left on the card. Too much energy for me when I'm so busy having fun.
I always use American Express travelers checks. Once, I lost them about an hour off the plane. What a way to start a disney trip! It was just like the commercial. I had replacements in hand in a few hours. I love them!
I have never had a problem cashing them in Disney. Off site a few times I have been asked for i.d. Usually I try to cash what I think I will need for the day at the front desk. I've had them accepted at all stores, restaurants, stands, even by the taxi driver. Never a problem.