I think this question is probably more appropriately answered by people who have a corporate amex account...whereas I have a personal account.
The amex that I use most frequently is the Costco TruEarnings Amex that earns 3% on dining, always. No limit. Sometimes Discover will run promos (like Oct/Nov) where restaurant dining will earn 5%, max at $500 spent or $25 reward. Then I'll break out my Discover card. (I've got 2, so I can double my reward before it maxes out.) Anyway, I was just at Mortons with a $300 bill and nope, they don't take Discover. And I was saving for that one too. Was bummed, but broke out my Amex instead. Not a big deal.
Doesn't influence my decision to eat or not eat at restaurant unless they don't take credit at all...I don't like paying for anything in cash if I don't have to...in fact I used to drive across down to Jack In the Box because they take CC's and McDonalds and BK don't.