Apple Pay is super useful for a US-based person while traveling internationally because Apple Pay supports CDCVM. This means that if you have a card that ordinarily requires a signature at the point of sale in the US, you can can use that card in Apple Pay, in Europe or anywhere else, without signing. If you use the physical card, you have to sign. If you try and use the physical card at an automated terminal that doesn't support CVM Signature, you can find yourself in a position where
only the Apple Pay version works.
CDCVM also generally doesn't have a contactless floor limit meaning while a contactless card may have a $100-200 cap for transactions, Apple Pay usually doesn't have a cap. Even when local contactless cards may be declined! I say usually because the terminal has to have been updated over the last few years to negotiate CDCVM, which they will in time.
I would highly recommend starting with Apple Pay abroad and only if it doesn't work falling back to a physical card because you will have a far better experience.
