Lord Ram taught us to fight for personal rights. When his wife was abducted by Ravana, he fought to bring his wife back.
Lord Krishna, on the other hand, fought first part of life during childhood for personal and family rights and killed Kansa but in his later part of life, fought for others. In Mahabharata, he helped Yudhishthir and his brothers to get back the kingdom and take revenge of their wife’s ( Draupadi) insult.
Lord Buddha, on the other hand, worked for the welfare of the society.
Lord Ram had a personal enemy. Lord Krishna had personal enemy only in the first part of his life, in the later part,Krishnahad no enemy. Lord Buddha had no enemy altogether.
Out of ten incarnations of Lord Vishnu, Ram is 7th, Krishna is 8th and Buddha is 9th.
The evaluation of Avtar means that your life starts with your personal achievements and then you start working for others and then for the society.
First you learn to take care of your needs, followed by that of others and finally of the society.
Ramayana and Mahabharata, Rama killing Ravana indicate killing the ego of the self;Krishnahelping killing Duryodhana means helping killing the ego of others and Buddha means creating a egoless society.
In terms of internal
The above interpretation is my own and has nothing to do with hurting sentiments of any religion.