I was really tempted to put theses in mammals because the main body is that of a lion. However their head (and so brain) is that of an eagle and the real clincher is that they watch from eggs. So...Gryphons are birds.
These are even more bird than the gryphons. Absolutely in the Bird section. They do have cloven hooves as back feet and antlers so are part mammal. But they rest in nests, lay eggs and definitely are covered in feathers.