Shedding
Their coats shed differently: the Great Pyrenees moults most as the seasons change, the Tosa sheds through the year.
Grooming
The Great Pyrenees needs more grooming, daily brushing, where the Tosa needs a brush once a week.
Exercise
Plan for a moderate amount of exercise with the Tosa, and a modest amount with the Great Pyrenees.
Temperament
They differ most on voice (Great Pyrenees: very vocal; Tosa: quiet) and on affection (Great Pyrenees: affectionate on its own terms; Tosa: likes its own space).
Alike
They are much the same size as adults, about 65 kg (143 lb) for the Great Pyrenees and 61 kg (135 lb) for the Tosa.
Alike
Both are rated the same on independence: decides for itself.