1 Sri Rama and Sri Krishna are both Poorana Avatars

Both Sri.Rama and Sri Krishna are poorna Avatar, Sri. Sri Rama sharing his Kalas with his brothers, whereas Sri.Krishna himself a poorna avatar. (Regarding Kalas - the difference of 12 versus 16 has been a much talked subject of interest among vaishnavas.)

As per the science of incarnations, Sri Rama is born is solar dynasty and Krishna in Lunar dynasty. Sun assumes it's completeness after 12 solar cycles whereas Moon becomes complete in 16 phases (full-moon). Being born in a solar dynasty the maximum radiance is achieved when 12 cycles are fulfilled and the same logic of 16 holds true in lunar dynasty. Hence, SriRama & Sri Krishna is complete, with nothing to add more or loose any.)

(Some may argue Sri. Sri Rama Avatar as Leela Avatar and Sri.Krishna Avatar as Poorna Avatar).

2. Sri. Sri Rama and Sri.Krishna Birth details

Sri Rama was born in Ayodya, whereas Sri Krishna was born in Madhura
Sri Rama was born on Navami, (number 9) because he is Maryada Purshottam. I.e. the one who will not deviate on his path will follow one rule all the time.

Thus nine represent whatever is the outcome, I will not deviate. (Which is in line with Sri Rama philosophy)

Sri.Krishna was in Astami, (Number 8) Sri Krishna is Purna Purshottam. So will do what the time and situation has to offer him. There is no set of rule for Sri.Krishna.
Thus number 8 does not follow any pattern if it goes down it will go down and suddenly again goes up. So number 8 follow the time and circumstance and re-act accordingly. That’s what Sri Krishna has done throughout Mahabharata.

Sri.Rama lived in Treta Yuga when morality was at the highest after Satya Yuga. Sri.Krishna lived in Dwapara Yuga close to the onset of the Kali Yuga when the morality was at the lowest. Sri.Rama preserved and guided humanity thru his selflessness and single mindedness. On the other hand, Sri.Krishna adopted radical ways to preserve and guide humanity thru goodness

3 .Appearance

Sri.Rama is not very different in appearance from Sri.Krishna. He has a bluish skin tone, similar to that of Vishnu and Sri.Krishna. He is usually shown in a standing posture, with a smiling countenance, holding a huge bow in His left hand and a quiver of arrows tied to His back. The most popular portrait of Sri Rama is that with his Consort, Sita, standing on His left; blessing His faithful monkey attendant, Hanuman, sitting at His feet on the right; His brother, Lakshmana, standing just a little behind Him, to His right. Being the Prince of Ayodhya, he is the shown adorned in all royal finery, with the usual 'tilak' on His forehead.

Sri.Krishna is depicted in various ways, during many stages of his life. But one of the most common images of Sri.Krishna is that of a cowherd boy leaning against a cow, playing His instrument, the flute. The word ' Krishna ' itself means 'dark' or 'black' in Sanskrit. It also means 'all-attractive'. Many works of poetry describe Krishna as the 'one whose complexion is tinged with the shade of dark clouds'.

While Sri.Rama is depicted as a very serious avatar, Sri.Krishna is seen as a playful figure, performing many miracles, stealing the hearts of young Gopis with his enchanting music, romping around with His Eternal Lover, Radha and so on. It is only the Bhagavad Gita that portrays Sri.Krishna in a somber light, that of a Divine Teacher.

4. Marital Fidelity

When it comes to a question of marital fidelity, Sri Rama outshines Dwarakanatha. Sri.Rama is the one who is Eka patni vrathan; Sri .Krishna has however two wives, Rukmani and Sathyabama

5. How they lived

Sri Rama lived like a human being hiding his parthva guna; Sri.Rama never ever wished to kill the enemies; from the very first thaatakai, he hesitated to kill her as she was a woman; He let Maareecha go away; while he killed subaahu; He even wished to forgive Ravana and gave ample chances for him to surrender. Whereas Sri. Krishna started killing His enemies and demons from the age of 10. Lord Krishna showed His parathva guna like lifting the Govardhana hill and killing asuras, all before the age of 10

6. Character of Sri.Rama and Sri Krishna

a) When we think of Sri Rama, what comes to our mind immediately is the upright figure, who would rather give His life, than speak untruth; in comparison, Sri Krishna emerges a professional fibber, right from childhood. No wonder Sri Andal characterizes Him as ‘ElA poygaL uraippan’ (Master fabricator of untenable lies)

Sri Rama’s honest ideals shine, making Him a paragon of virtues, and the personification of ‘Dharma’ or righteousness. Even His sworn enemies admit this, as is proved by Maricha’s words, ‘Ram o vigrahavan dharma:’ nobody in their right mind would ever accuse the Prince of Ayodhya of any moral turpitude, however slight. It is impossible not to love such a person.

Sri.Krishna involves himself without being involved; Sri.Krishna is manipulative and can trick people to do what is Dharma. He is a catalyst energizing others into action.

b) Sri Krishna is Svayam Bhagavan form. It means He is the first and the last; it is the spiritual form of God, His ultimate form. Sarva karana karanam, as Lord Brahma described Him in Brahma Samhita - the cause of all causes. He is the God Himself in the most confidential form, Bhagavan. Sri Rama is incarnation indeed, but He is the Lord Himself too. All expansions of the God, Krishna have its origin from Him.
Balaram is His first expansion. Lakshman is His form as the brother of Sri Rama. Always remember something, Achintya bheda-abheda tattva, it means "inconceivably, simultaneously one and different". The human mind cannot conceive how Krishna is everywhere as Paramatma, all pervading form; what is Brahman, his formless expansion; how He expands in millions of expansions and forms.
Sri.Krishna was never shown worshiping any Gods like Sri Rama who worshiped Surya and Lord Shiva

c) Sri Krishna preached like a teacher, He was anything but emotional.
While Sri Rama also practiced. To those who surrender to Him, Sri Rama is infinitely dearer to the heart, for His whole life was devoted to Saranagata Rakshanam, as borne out by Sri Vibhishana Saranagati and others portrayed by Srimad Ramayana
Sri Rama’s unquestioned valor, which is ever on display. His arrow is as straight as He is, and as effective on His enemies. And the wars He fought were all above-board, role models of ‘dharma yuddha’. Sending back an un-armed, battle-weary Ravana to come better prepared the next day, was indeed an act of incomparable courage. This Shows Sri.Rama’s compassion and emotional.

And Sri Rama belongs to a line of Emperors, for whom Saragagata Rakshanam was a Kula dharma; Sri Rama is an ideal character; In Sri.Rama avatara He practiced all dharma appropriate for His character. He never compromised on that
In Sri Krishna avatara He taught us what He already practiced in Sri Rama avatara. (Bhagawad Gita) Sri Krishna is an actor and strategist. ; Sri.Krishna involves himself without being involved; Sri Krishna is manipulative and can trick people to do what is Dharma. He is a catalyst energizing others into action.

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Sri.Rama is a doer; he acts for his ideals and is therefore called marayada purshottam. Sri.Krishna on the other hand, is an incomparable actor; he turns the whole world into his stage. He plays a friend and a foe without being involved in friendship and enmity. Sri.Krishna is called leela-purshottam. He accepts all contradictions and ambiguities of life. He isn’t afraid of them

Sri. Sri Rama lived to please others through out his life; Sri.Rama is a role model for every one in conducting ones own self.

What Sri Rama did can be copied and practiced by every one.

Sri. Rama's life is simple and open page for every one to understand; Sri.Krishna symbolizes love, grace, spontaneity. He showered love all around. He taught us all shades of Love. He was never bothered about his political or social image or his enemies. He was cool and collected and did what was necessary in time with immense grace.

Sri Rama portrayed the compassionate nature of Vishnu and Krishna portrayed omnipotence.

Sri Rama brought down rational and sane mind into the earthly consciousness and Sri. Krishna brought down the Over mind consciousness. Sri Rama's role was more of getting the earth rid of its evil forces. Sri Krishna is there to drive evolution towards the great Ananda.

Sri Rama for establishing dharma while Sri Krishna mainly is for establishing prema

Sri Rama avatar is to show how human being should be.

Sri Krishna avatar is how God will be.

SriRama was loved by his wife, parents, brothers, subjects; Sri Krishna was loved by his wives, brother, Pandavas and of course the girls and cows too.

If Sri Rama name has become associated with Hindu Nationalism and held up as a model of Hindu devotion to caste and the rules of dharma, whereas Sri.Krishna, the Indian Hercules, as He is styled by Megasthenes, the most popular hero of India.

Sri.Rama and Sri.Krishna are completely opposite in nature. Sri.Rama was born in the noon and Sri.Krishna midnight. Sri.Rama was always a sishya, i.e. a student throughout His life, whereas Sri Krishna was always a teacher. He was a Guru even to His mother. Sri.Rama respected every one. Every one respected SriKrishna.

Sri.Krishna is Svayam Bhagavan form. It means He is the first and the last; it is the spiritual form of God, His ultimate form. Sarva karana karanam, as Lord Brahma described Him in Brahma Samhita - the cause of all causes. He is the God Himself in the most confidential form, Bhagavan.