Monel strings aren't as bright as phosphor bronze. Their high end is smoother and more controlled.
That controlled high end makes Monel a favorite for recording. Many players and engineers like how the smoother highs and controlled harmonic response reduce harshness and excessive pick attack. Fingerstyle players like them for the same reason, since they keep note clarity without excessive brightness.
Monel strings are especially popular for blues, folk, Americana, roots music, fingerstyle and vintage-inspired acoustic playing.
Many players also find that Monel strings keep their tonal consistency longer, because the nickel-copper alloy resists corrosion very well.