The Frazier IV-a is a 2-way speaker design, utilizing a Helmholtz resonator port, but with pretty basic drivers. The Heresy (I, II, or III?) is an un-ported box (but not sealed) with a 3-way set-up of better drivers than the Mk IV. Both use horn drivers and direct radiator woofers (10" for the Frazier, 12" for the Klipsch).
With your eyes closed, and both speaker pairs at spec and optimally placed, I'd put my money on the Frazier.