Garuda the king of birds is the vahana of Sriman Narayana and his consort Goddess Lakshmi. He carries them on their shoulder and flies from one place to another. He will be on the skies hence known as Big Thiruvadi. Likewise Hanuman king of vanaras carry Lord Rama, Sita and Lakshmna on his shoulders from one place to other in land. Hence he is known as Small Thiruvadi. Any mythological evidence for this? If so in which purana?
Garudazhwar is known as Periya Thiruvadi, since he is the Vahanam (vehicle) of Sriman Narayana and also all of his incarnations such as Krishna. But Hanuman is known as Siriya Thiruvadi since he is the vehicle/devotee of only one of the incarnations of Vishnu, namely Rama.
This practice of calling Garuda as Periya Thiruvadi and Hanuman as Siriya Thiruvadi is followed in the Srivaishnava tradition. Hence, there is no Puranic reference for this. Also, it is important to note that these terms are in Tamil, and Puranas are written in Sanskrit.