Krishna and Rama
Krishna and Rama are both vishnu-tattva, in the category of the Supreme Person. But one difference is that Krishna is the origin of all other incarnations of God, and Lord Ramachandra could be said to be one aspect of Krishna's personality. Lord Rama's pastimes are those of a valiant king, and His superhuman activities are those of a great hero.
Krishna also performed incomparable feats in his killing of demons in battle when He was acting as Prince of Dwaraka. But His pastimes with His devotees in Vrindavan show an even more private side of His personality, without any trace of the majesty associated with His pastimes in Dwaraka or those He displayed as Ramachandra.
The relationships Krishna has with His devotees in Vrindavan isn't mixed with any of the awe and reverential worship that characterizes most relationships in Vaikuntha, Dwaraka, or Ayodhya. Krishna's Vrindavan devotees have such pure love for him that they treat Him as an equal—either as a friend, lover, or son. It is said that in Dwaraka, where Krishna appears as royalty, His majesty overpowers His sweetness. But in Vrindavan, where Krishna appears as a simple cowherd boy, His sweetness overpowers His majesty.
As Ravindra-svarupa dasa (William H. Deadwyler, Ph.D.) mentions in the ISKCON Communications Journal, #2.1, January/June 1994:
"According to Gaudiya Vaishnava theology, God has both a public and a private face. When He manifests his power and majesty (aisvarya), He is known as Narayana and is served in awe and reverence. When He sets aside His lordship, however, and allows his beauty and sweetness (madhurya) to overpower his majesty, He is known as Krishna, the all-attractive. In order to enjoy intimate exchanges of love, Krishna causes His confidential devotees to forget that He is God, so that they may serve Him in a fraternal, parental or conjugal mood."