I don't think any of us are buying things and purposefully damaging them or having them stolen if that's what you're referring to, but if I need to file a claim I'd much rather do it with Amex because they make it so easy in the event that you ever have to, vs Chase which makes you deal with eclaimsline or whatever 3rd party they outsource it to. And when you say the CSR has the same coverage, that's mostly true, but not entirely. Chase's purchase protection excludes lost items. They define this as "Items that mysteriously disappear with no evidence of a wrongful act", aka, lost/misplaced/etc. While that might not seem like an important distinction, if something were to happen to a new pair of Bose headphones, or something, I think we travelers are a lot more likely to misplace them than have them stolen or damaged, which is what Chase's coverage would require happen to them.

Knowing that distinction and having used my Amex saved me about $200 a few months ago that I otherwise would be out of pocket for had I used a Chase card.