Regarding SATB: Such scoring tends to have a vertical (harmonic) emphasis, rather than ensuring that each line is really melodic and interesting. There is also no indication which line has the most harmonically suggestive bit at any particular time, as it varies moment to moment.

A good two-part harmony differs substantially from what you find in a four-part harmony. The harmonist must shift about flexibly, and intuitively weigh a number of sometimes conflicting factors. When do you need a close sound (like parallel thirds), an open one (like fifths or sixths), unison, drone or part crossing? When do you need to break a pattern? When is it important to stress the third of a chord, to distinguish major and minor? When do you instead need the seventh, sixth or even ninth/second? When do you need to arpeggiate in some fashion, to provide a fuller harmonic context? When do you need to provide a rhythmic or contrapuntal contrast, or an echo? When do you just need to shut up? A good harmony line, viewed in isolation, is often more wild and interesting than the melody line.

The concertinist is more fortunate than a harmonizing singer, because obviously he doesn't have to limit himself to a single harmonizing note. But if you want to learn the essence of good melodic accompaniment, listen to great duos singing unaccompanied. I recommend the Silly Sisters (Maddy Prior and June Tabor), and John Roberts and Tony Barrand.

Hope I didn't get too "pedantic". ;-}