But it should be the same shouldn't it? I wouldn't have thought that there would be a difference. Apple Pay is Apple Pay.
I also can't find the option to turn on or off notifications for what it's worth.
I thought so too... but wasn't getting notifications and then I saw on the Amex website it's for "iPhone 6 and above":
https://www.americanexpress.com/us/content/apple-pay/
which seemed odd...
Are your notifications coming from the Amex App (which has its own way to set notifications for each card in settings) or the Apple wallet?