My take: 6/8 works because the motive fits perfectly in one measure with a strong and weak compound beat. Think about the implied metric emphasis. 3/4 would place too much emphasis on "night". 6/8 is much smoother. Why is "O, Holy Night" in 12/8? 3/4 would be simpler to read for young musicians, but 6/8 is not that much of a stretch to teach from this, especially since the melody is familiar. The graphic connections would be very clear. I'm interested in hearing your opinions!