Compared to the Honda HRR models with a steel deck, the Honda HRX has a longer warranty, including a lifetime warranty on the composite (NeXite) mower deck. The HRX has the larger, more powerful GCV190 (190 cc) engine. The HRX has larger wheels, bearings on all four wheels, a super-nice hydrostatic transmission, the list goes on. The HRX is Honda's top-of-the-line model, and the HYA with the hydrostatic trans. is considered top-shelf. Only the electric start version is technically "nicer" for another $100.
Not sure about that price, $488 seems very low(!) The list price on the HYA is $799. Maybe this is a refurbished one that has been returned? Double-check, as the return policy on refurbs varies from store-to-store, and is not the usually generous 30 days on brand-new units.