The live rehearsal recording might sound warmer and more natural on a decent pair of headphones, but it'd sound like complete mush on AM radio. The very sparse, crisp mixes of the 80s can sound harsh and synthetic to a modern listener, but they sound superb on a cassette boombox.
Most pop mix engineers habitually toggle between a high quality monitoring system and a "grot box" speaker (often in mono) with good transient response but very limited frequency range. They understand that their job isn't to produce a mix that sounds good in the studio, but a compromise mix that sounds as good as possible across a wide range of low-fidelity playback systems.
Modern mixes tend to be more neutral because of the general improvement in playback fidelity. Still, a competent pop mix engineer is giving a great deal of thought to how well a mix will work in a noisy restaurant or through the built-in speakers on a TV. They're thinking about people listening in the car or listening through one earbud.