Among Vishnu’s avataras, Rama and Krishna avataras are considered poorna avataras. Balarama avatara is considered an amsa avatara, and Parasurama avatara is an avesha avatara. Rama and Krishna were born in this world and lived for many years. The Vishnu Sahasranama, which extols the Lord, speaks of His various qualities as seen in His avataras. Parasara Bhatta wrote a commentary for the Vishnu Sahasranama titled Bhagavat Guna Darpana. While the entire Vishnu Sahasranama may be said to be about Krishna, Parasara Bhatta gives 32 names as referring to Rama, and 90 names as referring to Krishna, said M.A. Venkatakrishnan, in a discourse.
In the Rama and Krishna avataras the qualities of sauseelya and saulabhya, respectively, are highlighted. As Rama, He was simple, despite being of royal birth. He befriended those lower in status, like Guha, for example. Even a monkey was accepted as a friend. Rama was prepared to get down to the level of those who were not His equals. But Krishna went further. He was prepared to lower Himself, and place Himself on a lower footing than those whose status was less than His. He became a messenger of the Pandavas.
Parasara Bhatta had a partiality for the Rama avatara. Once he was asked why Rama did not act as anyone’s messenger, whereas Krishna did. Parasara Bhatta replied that no one dared to ask Rama for such help, because Rama was a king. But Rama had an urge to be a messenger. That is why He decided that in His next avatara He would not be born as the son of an Emperor. Making oneself lower than others who do not enjoy a high status, is saulabhya, and this quality stood out in the Krishna avatara.