Size
The Miniature Schnauzer is a little larger on average: about 6 kg (13 lb) as an adult, against 5.1 kg (11 lb) for the Yorkshire Terrier.
Shedding
Their coats shed differently: the Miniature Schnauzer holds loose hair until it is brushed or clipped out, the Yorkshire Terrier sheds through the year.
Grooming
The Yorkshire Terrier needs more grooming, daily brushing, where the Miniature Schnauzer needs a brush once a week.
Exercise
Plan for a moderate amount of exercise with the Yorkshire Terrier, and a modest amount with the Miniature Schnauzer.
Temperament
They differ most on affection (Miniature Schnauzer: affectionate on its own terms; Yorkshire Terrier: a lap or leaning dog) and on independence (Miniature Schnauzer: cooperative, with its own ideas; Yorkshire Terrier: decides for itself).
Alike
Both are rated the same on voice: very vocal.