In terms of behaviour, Sri Krishna and Rama are poles apart though both are the Avatars of Vishnu.
Lord Rama was an Idealist.
Krishna a Pragmatist.
For Rama Means were as important as the End.
For Krishna End justified the Means, in upholding Dharma.
Rama grew up amidst Royalty,
Krishna among cowherd never became a King, remained a prince throughout his life.
Krishna married two women,Rukmini and Sathyabhama, while Rama was steadfast only to Sita.(read my post 16,000 wives of Krishna).
Rama was personally attached to His parents, wife, friends.
Krishna detached attachment.
Krishna gained nothing for His labours.
Rama gained His Kingdom and regained His wife.
Rama was so attached to Lakshmana, His brother that He breathed His last when He heard Lakshmana left His Body.
Krishna paid Rama’s debts.
Rama killed Vali ,hiding behind tress, Krishna was killed by a Hunter in stealth.
Laksmana served Rama.
Krishna served Balarama who was an Avatar of Lakshmana in Dwapara Yuga.
Krishna was so detached, He endorsed the destruction of His Death and of His Clan, due to a Curse by Kandhari.
According to Mahabharata, the Kurukshetra war resulted in the death of all 100 sons of Gandhari. On the night before Duryodhana’s death, Lord Krishna visited Gandhari to offer his condolences. Gandhari felt that Krishna knowingly did not put an end to the war, and in a fit of rage and sorrow, Gandhari cursed that Krishna, along with everyone else from Yadu dynasty, would perish after 36 years. Krishna himself knew and wanted this to happen as he felt that the Yadavas had become very haughty and arrogant (adharmi), so he ended Gandhari’s speech by saying “tathastu” (so be it).