Trying to define all cheeses as having a same flavor profile is impossible, due to the sheer quantity, as well as variances in animal breed type, animal diet, seasonality, maturation, and terroir (loosely meaning the specific environment of a place, like climate, soil, altitude, etcetera that cannot be exactly replicated anywhere else).
However, flavor profiles of the milk types are often described as follows: Cheese from Cow's milk has the greatest diversity in flavor resulting from the large variety of vegetation consumed by the animals during summer months. Most generally, it's thought to be buttery, grassy, and sometimes sweet. Cheese made from Goat's milk is characteristically tangy and acidic. Cheese made from Sheep's milk has a rich, nutty, oily quality about them. Finally, cheese made form Water Buffalo's milk has a wet hay, lactic flavor profile.