I received the exact same level of service from Discover over the last 2 years. Lose my card? They overnight it to me at no additional charge. Fraud charges? Never had an issue with a dispute.
I've found Amex's concierge to be okay and their travel product prices to be absurdly high. The only reason I keep my Platinum card is because I get $200 in Southwest gift cards each year with their airline reimbursement, and they reimburse me occasionally for my Global Entry membership renewal.