I had Platinum and the option of the Centurion (black). People I know with Centurion cards actually just don't use them that much after an initial "fun" period of showing off. Using them at clubs, for instance, is just a great way to get extra charges thrown in, since people will guess you aren't carefully reviewing your statement and have extra money.
OTOH if you don't mind coming off as a dick, you can pull out a Centurion card and try to bully/bluff people with a "don't you know who I am" kinda deal. Though I did love the one time a friend tried this and the clerk just laughed and said "we don't take Amex". Also, other banks are issuing "Black" cards so there's a lot of people trying this not even being Amex holders.
Centurion used to come with more benefits, but they've been pulling them back and making it more of a show-off "I'm so elite" kind of thing. (A big blow was losing Continental elite status, since United is Chase's bitch.) They're building out airport lounges now to help compensate. And in Toronto Pearson, because Canada is just so incompetent, airlines don't have faster lines for security, just Air Canada and Amex. Rather annoying if you're a United 1K or otherwise paid for first class. That's probably the only reason I'd consider getting an Amex card again.
Nowadays, even random VISA cards will have concierge services, because it's fairly cheap, underused, yet makes people feel special. And for the cost of a Platinum card ($495 for primary, then $195 I think) you can use a lot of other services. And Centurion cards were $5000/$2500. I think you could just carry $5000 in cash and get the same kind of "respect".
(I haven't used Amex in years. Despite paying on time, always, and having a runrate of over $250K a year, they did a financial review, requesting my tax/employment records. I told them to fuck off and that was that.)