If I have a problem with a merchant, will Amex treat me any better if the charge is on a personal Platinum card versus the Brilliant card?

I have both, and on paper the policies are the same: return protection, purchase protection, and extended warranty. (I've used R.P. twice on Brilliant and it went well.) However is there some unwritten benefit to platinum given how they treat it as a flagship card? Apologies to Centurion members.