OK, in the room at the show, what you hear is a combination of
A. The sound of the instruments onstage. Drums, Amps
B. The PA. This is a mix of instruments to balance out the different volumes coming off stage. Vocals, kick drum, some bass, keys are often predominant in the PA.
So, think of mics in the audience as A+B.
If you combine audience mics with a soundboard, you are emphasizing the PA mix by adding in more PA (B) to an already balanced mix (A+B).
If you combine onstage mics with audience mics, you are emphasizing the onstage sound by adding in more Stage (A) to the already balanced mix (A+B)
If you combine onstage mics + a soundboard you can mix the same balance of Stage (A) and PA (B) to get a clean sound (A+B) but the only audience you'll get is bleed into the onstage mics. This is often too dry for one who prefers audience tapes.
The Six channel approach solves this. Onstage (A) + Soundboard (B) + Audience mics (A+B).
I'm not saying that audience and soundboard can't sound good, but that it has a flavor due to which sources you are mixing.