I have been a Platinum AmEx member since 2000 and have had my Centurion for 2 years now along with the Platinum (business reasons). Honestly For majority of the perks such as airline credit of 200 dollars and specials on hotels and such its about the same.
What is different is the concierge service but most importantly your airline status. See having a US Airways Platinum status makes you a Star Alliance Gold member as well. So if you fly any of the Star alliance airlines you get a few extra perks (Priority check-in and boarding, Extra baggage allowance, and a few more small perks). Whats nice about US Airways Platinum is that 4 days before your flight they will check to see if there are available first class seats and if so you get it first before silver or gold (more on that here US Airways | All about Preferred
Secondly since you are also a Platinum medallion on Delta you get a heavy amount of perks available to you through Delta airlines. As the status is high you share some of those benefits (once again) with the Sky Team airlines. Pretty much if you fly (or rent cars) constantly you might see a difference but if you want points and such don't expect to recover 2,500 USD in benefits through it (unless you plans to spends some crazy cash. I enjoy the exclusivity but am now wondering if having a card that is for show (besides my perks I have juiced completely dry over the last 2 years) is worth it.
These are fair sites that compares them (that has been mentioned before I know) http://www.askmrcreditcard.com/creditcardblog/amex-platinum-vs-centurion/
This site gives a pretty good (and current) breakdown on the diffrences between the two.http://www.jblackbelt.com/comparisonsmain/comparisons/gold-platinum-centurion.html
Some correction on this site is that now (since Sept 1st) all additional cardholders are 2500 USD as well and also you can ONLY have 2 additional Centurion cardholders on 1 account. This was due to Centurion trying to thin out their leeching additional cardholders who are just in it for the thrill of having the card (this is now mostly because of the numbers rising so they are trying to limit new cardholders to keep the value and exclusivity on the card).