Clovis, there's no such rule-of-thumb which has a factual basis. There's simply nothing to support a claim that a "simple" integrated pre/power combination somehow is audibly better than a receiver loaded with bells and whistles. If the amplification takes place with audibly flat frequency response and inaudibly low noise and distortion, which is commonplace in even modestly-priced receivers these days, nothing more is possible in the amplification process.

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Enjoy the music, not the equipment.