"Or is the point a subtler one about the voicing (spacing) of the chords?" writes a Member.
We do not know about the specifics of writing for the organ, and cannot contribute anything on that specific point.
But the texture and voicing of music, or the distribution of the parts, is tremendously important for the effect of harmony.
Schubert was one composer who was always very careful about this, and it shows, and it is effective. We think that it will be evident especially to men who PLAY rather than listen to his music.
Another interesting composer in this regard was Bach himself. So often - in the keyboard concertos for instance - we find him moving to a chord the distribution of which is rather different from the normal expected case, but we know he means to do it, and what a pleasant sensation he gives us all thereby!
At least two systems of musical analysis have grown up - one for harmonic music (the "transpositionally equivalent sonority") and one for the pan-tonal (called "Forte's normal order of a pitch-class set"). They involve the picking out of the simultaneously sounding notes and arranging them in a fixed prescribed close order, which procedure is of assistance in their categorization and comparison. But important textural information is lost thereby and the "equivalence" is more imaginary than real.
Specifically, what matters is the way composers cleverly take into account the effect of all the partials and overtones in combination, is it not? - rather than the effect of simply the explicit struck or sounded notes.
And the disregard of voicing is one of the many problems inherent in simple-minded serialism.
