A couple considerations from my notes, as I was just comparing the Platinum, Executive, Prestige, and Chase Presidential Plus:
Premium Global Assistance. Both cards have stated coverage for medical transportation/evacuation. As unlikely as such an event is, it's notable that by description, the cardholder is covered regardless of whether a trip is paid for on the Platinum. There are also no limits specified for emergency transportation.
Premium Roadside Assist. Amex Platinum covers costs for up to four vehicle events per year. I've used this once already in my first few months and probably saved over the $50 they describe as the limit.
Centurion, Airspace, and Delta lounges. Losing AA/US does suck for domestic travel. I'm going to enjoy of double coverage with my executive though and see how much I would lose out going Platinum-only. Overall coverage for international does seem to skew in Amex's favor, and the above do round things out in country.
Fine Hotels & Resorts perks and online booking. You can actually browse and book all of this yourself online, which is nice.
Gold Hotel Collection. Accessible to Platinum as well.
Hertz benefits. Minor one, but probably more useful domestically versus Sixt.
Extended warranty. Although coverage payouts are identical, Amex adds a year up to a total of
5 years maximum. I can't find specific terms for the Prestige. Assuming it is the same as my Executive World Elite, it has a pretty oddball limitation, which I assume means a maximum of only 2 years coverage:
"If either the original manufacturer’s (or U.S. store brand) warranty or the service contract covers more than twelve (12) months, this benefit will not apply."
Car rental insurance. Platinum covers vehicle value up to $75k, but more relevant the included secondary coverage appears (according to my benefits details) to include AD&D and small amounts of excess medical and property coverage. Amex also provides
primary insurance at a flat rate per rental.
MasterCard coverage requirements. According to the fine print, many of the travel insurances (including car rental) apparently require booking through their designated travel agent. Amex seems much more flexible.
It might be that the Prestige backs its benefits very differently from the Executive, but from what I can tell they both derive many of the competing benefits from the World Elite MasterCard program. This seems on paper to be designed to duplicate many Platinum benefits. However, the fine print and obscurity of actually using any of them makes me skeptical of their quality. My perception is that Amex is more proven.