"The heads of Beauxbatons and Durmstrang will be arriving with their short-listed contenders in October,"
-- Albus Dumbledore (GF12)
The Durmstrang Institute’s ship appears in the Lake. The people from Beauxbatons arrive in a carriage pulled through the sky by Abraxans.
The Durmstrang delegation rises up out of the water and the Beauxbatons delegation comes down from the sky. This may suggest attitudes or school culture. Note that among the four Hogwarts houses, Ravenclaw is aligned with air/sky and Slytherin's aligned element is water (TLC). -BB
The same carriage pulled by winged horses returns in 1997 to bring Madame Maxime to Dumbledore's funeral (HBP30). -BB