Centurion Card (Black Card) vs Platinum Card for Morgan Stanley

Every figure below is from the same dataset Miles computes its recommendations from. Rows the two cards agree on are collapsed at the bottom.

Economics

Dollar figures are per year unless the row says otherwise. Ongoing annual value is Miles' estimate of what the card adds per year after its annual fee: statement credits discounted for realistic use, benefits, and earning above a strong flat-rate card on a typical spending profile. First-year value is a separate net figure that includes the welcome bonus. A welcome bonus shown at its advertised maximum may not be available to every applicant; that figure is not marked as stronger. ★ marks the stronger comparable figure on other rows, and no row is marked when either figure is unknown.
Figure	Centurion Card (Black Card) American Express	Platinum Card for Morgan Stanley American Express
Annual fee	$5,000	Best: $895 $4,105/yr less
Ongoing annual value, after fee	−$4,379	Best: $906 $5,285/yr more
First-year value	−$4,979	Best: $1,041 $6,020/yr more
Authorized user fee	$5,000	Best: $0 $5,000 less

Sign-up Bonus

The current welcome offer as recorded in the dataset. No winner is marked: a bonus is points times a valuation times a spend requirement you may or may not clear, and the first-year value above already prices it.
Offer	Centurion Card (Black Card) American Express	Platinum Card for Morgan Stanley American Express
Current offer	Invitation-only; no public welcome offer	80K after $12K spend within first 6 months

Earning

Percentages are the return on a dollar spent: the multiplier times what Miles values those points at. ★ marks the higher return on a row. Categories only one card earns a bonus on are marked for that card; the other earns its base rate.
Category	Centurion Card (Black Card) American Express	Platinum Card for Morgan Stanley American Express
Flights booked directly with airlines or through Amex Travel (up to $500K/year)	—Unknown	Best: 5X7.5%
Prepaid hotels booked through Amex Travel	—Unknown	Best: 5X7.5%
Purchases of $5K+ (up to $500K per calendar year)	Best: 1.5X2.2%	—Unknown

Benefits

Statement credits, lounge access and elite status as listed in the dataset; protections are counted, not listed. No winner is marked: twelve small credits are not more than two large ones, and the row that prices them, ongoing annual value, is under Economics.
Benefit	Centurion Card (Black Card) American Express	Platinum Card for Morgan Stanley American Express
Statement credits	CLEAR Plus: $438 (Annual Calendar Year) Saks Fifth Avenue: $250 (Quarterly Calendar Year) Equinox: $300 (Monthly) Uber Cash: $15 (Monthly) Global Entry/TSA PreCheck: $120 (Every 4 Years)	CLEAR Plus: $219 (Annual Calendar Year) SoulCycle At-Home Bike: $300 (One Time) The Hotel Collection: $300 (Semi Annual Calendar Year) Digital Entertainment: $25 (Monthly) Uber Cash: $15 (Monthly) Walmart+: $13 (Monthly) Airline Fees: $200 (Annual Calendar Year) Global Entry/TSA PreCheck: $120 (Every 4 Years) Resy Dining: $100 (Quarterly Calendar Year) Uber One: $120 (Annual Calendar Year) lululemon: $75 (Quarterly Calendar Year) Oura: $200 (Annual Calendar Year) Equinox: $300 (Annual Calendar Year)
Lounge access	American Express Centurion Lounge (unlimited) Priority Pass Select (unlimited) Delta Sky Club (when flying Delta) (unlimited)	American Express Centurion Lounge (unlimited) Priority Pass Select (unlimited) Delta Sky Club (10/yr) Plaza Premium Lounge (unlimited) Airspace Lounge (unlimited) Escape Lounge (unlimited)
Elite status	Delta SkyMiles Platinum Medallion	Marriott Bonvoy Gold Hilton Honors Gold LHW Leaders Club Sterling Avis Preferred Preferred Plus Hertz Gold Plus Rewards President's Circle National Emerald Club Executive
Protections	9	9

The same on both cards (6)

Rows where both cards state the same figure or the same earning rate. Nothing is marked, because there is no stronger side.
Fact	Centurion Card (Black Card)	Platinum Card for Morgan Stanley
Foreign transaction fee	None	None
Issuer	American Express	American Express
Rewards currency	American Express Membership Rewards	American Express Membership Rewards
Card type	Personal	Personal
Network	American Express	American Express
All other purchases	1X1.5%	1X1.5%

Which one is right for you

This page shows the difference. It does not pick: the winner depends on what you spend and what you already hold, and adding these figures up without knowing that would be a guess dressed as a verdict. Ask Miles and it computes the answer against your own wallet.

Ask Miles which to get