Shedding
Their coats shed differently: the Great Dane sheds through the year, the Great Pyrenees moults most as the seasons change.
Grooming
The Great Pyrenees needs more grooming, daily brushing, where the Great Dane needs a brush once a week.
Exercise
Plan for a moderate amount of exercise with the Great Dane, and a modest amount with the Great Pyrenees.
Temperament
They differ most on voice (Great Dane: quiet; Great Pyrenees: very vocal) and on affection (Great Dane: a lap or leaning dog; Great Pyrenees: affectionate on its own terms).
Alike
They are much the same size as adults, about 64 kg (141 lb) for the Great Dane and 65 kg (143 lb) for the Great Pyrenees.