In the UK (which broadly follows the same rules), I get 0.25% with a Visa and 1.25% with Amex. Sometimes there are introductory offers for a few months.
And as a result of that, Amex is often not accepted.
At least in the UK Amex interchange fees are not capped like Visa and Mastercard.
I only get cashback on my Amex, nothing with Visa or Mastercard; perhaps I could shop around but over 90% goes on my Amex so haven't bothered to.