Bhagwan Sri Ram is a complete(Purna) Avatar of Sri Bhagwan. In this Avatar Bhagwan had to show the full potential of a man as Ram and full potential of women as Sita. So he did not have to show any Godly qualities to get his message across. This is why Bhagwan Ram is called Maryada Purushotam (Ideal man) and same goes for mother Goddess Sita Mata. This is why Bhagwan Ram always said “My name is Ram and I am the son King Dashrath.” The complete Ramayan is put in written form as the epic Ramayan.
Bhagwan Sri Krishn is a complete (Purna) Avatar of Sri Bhagwan. In this Avatar Bhagwan had to show his full Godly qualities. He openly said that he is God himself. He revealed his complete form to Arjun when he revealed the sacred holy knowledge of Bhagavad Gita just before the war started in the battle field of Kurukshetra.