Generally similar benefits between Virtuoso, AMEX FHR and specific hotel travel agent rates like Hyatt Prive, Four Seasons Preferred Partners, STARS etc although AMEX FHR is the only one that guarantees 4pm late checkout. There may be also usually minor differences in the $100 credit offered. For example at IC Porto currently AMEX FHR gives $100 food and beverage credit, IHG Destined gives $100 hotel or resort credit and Virtuoso gives a complimentary lunch or dinner for two. Each program may also offer unique special offers like stay 3 pay 2 on certain dates. For IHG benefits/points I would think IHG Destined and Virtuoso rates are definitely qualifying and AMEX FHR is less consistent as rates can be prepaid or paid at the hotel and some of the bookings somehow look like they are from an online travel agency instead of travel agent. See this lengthy Marriott thread for various DPs either way.
Are AMEX FHR bookings eligible for MR points/nights?.