Wow. Two companies with which I would never intentionally do business. Having spent most of my professional life in financial services, these guys have some of the worst reputations.
Amex's system is a horrible deal. Much better off with MC or Discover.
I've had Amex since the 80's and I've had to use them with my expense account(s). They seem to be vicious when dealing with false charges which is nice, but they aren't without issues.
I had an instance where I was working at a refinery in New Jersey and got an email from Amex asking if I'd spent a few hundred dollars at a coin shop. I said no and they promptly shut the card down telling me they'd send a new one to my place of business overnight. I should mention I'm based out of Texas. But I had a personal Amex to fall back on.
The next day I got an email asking if I had spent a few hundred dollars at a golf pro shop on my personal card. I said no and they promptly shut that card down telling me they'd send a new one to my home within 5 business days. Great, now I have to fall back on my Visa which is tied to my checking account and I have to deal with corporate accounting to explain why I didn't use Amex.
I always thought that the problem must be on their end as I didn't have time to go anywhere other than the refinery or the hotel, of course, they'd never admit to that.
I've also had vendors refuse Amex due to their charging more for use of their system, but accounting loves detailed statements.
Other than the above I've never had any issues with Amex, I always pay everything off asap so there's no interest to worry about.
I had to get a Master Card because a few places in Canada wouldn't take either Amex or Visa.
I didn't know that Discover still existed, haven't had one in years since I've worked myself down to being debt free.
I still use Amex and a Costo Citi Visa for convenience's sake, and because if I have cash my kids can smell it on me and then it's gone.