I think only few avatars are know about their complete consciousness .not even Rama is complete avatar and Krishna is a one compete Avatar of Vishnu
Much later, Vishnu was incarnated as Rama, the prince of Ayodhya. After breaking the bow of Shivaat Janaka’s court, Rama, who won his wife Sita‘s hand in this manner, was returning from Videha with his family, including his bride to Ayodhya. Parashurama had heard about the valor of this young prince. He remembered his vow to exterminate all Kshatriyas (which had already been completed, but his memory was selective), and waylaid this party in a forest.
He said to Rama, “Do not be proud that you have broken the bow of Shiva. That bow had become rotten with disuse. It used to lie in a box in Janaka‘s court, and had not been used for ages. It is no wonder that it crumbled at your touch. Here, I have another bow of Shiva, given to me by the Lord himself. If you are really as strong as they say, string this bow and fire an arrow from it.”
Dasharatha, the father of Rama was alarmed. He knew of Parashurama‘s anger and his vow. He pleaded with the sage, “O great one, Rama is still a boy. He cannot do what you ask of him. He is virtuous and obedient. Do not destroy him with your anger. If you must fight someone, choose me. Spare the life of my child!”
Rama said, “Father, Do not worry. The sage has not asked me to fight him. He merely wishes to test my strength by stringing this divine bow. Permit me do this task. Perhaps I might be able to accomplish it.”
Reluctantly, Dasharatha was forced to give his consent. Rama took the bow from Parashurama and effortlessly strung it. He then affixed an arrow to it and drew the string back. He then asked the sage, “Sir, once an arrow has been affixed to a bow, it must be fired. What shall I use as target?”
At this point, the realization dawned upon Parashurama that his mission as an incarnation of Vishnuhad come to an end. In Rama he recognized the aspect of Vishnu. His pride was humbled. He said, “Let the target be my foolish pride! O Rama, you are verily the incarnation of Lord Vishnu himself. May your glory increase. Your fame will live as long as this world exists. You may keep the bow.” After this, the sage took leave of the party and went his way. At this point, the spark of divinity that was inside him, was transferred to Rama, who was now the incarnation of Vishnu.
Parashurama lived for a very long time. He was still active during the time of Mahabharata. He had taught Bhishma, son of Shantanu in the use of arms. (That story is narrated here). He also fought against his disciple, at the behest of Amba, whom Bhishma was refusing to marry. He was not successful in this task, his disciple proved to be equal to him in prowess.
Parashurama: Rama with the axe, appeared in the Treta Yuga. He is son of Jamadagni and Renuka. He received an axe after a penance to Shiva. Parashurama is the first Brahmin-Kshatriya in Hinduism, or warrior-saint, with duties between a Brahmana and a Kshatriya). His mother was from the Kshatriya Suryavanshi clan that ruled Ayodhya, of the line of Rama. King Kartavirya Arjuna and his army visited the father of Parashurama at his ashram, and the saint was able to feed them with the divine cow Kamadhenu. The king demanded the animal, Jamadagni refused, and the king took it by force and destroyed the ashram. Parashurama then killed the king at his palace and destroyed his army. In revenge, the sons of Kartavirya killed Jamadagni. Parashurama took a vow to kill every Kshatriya on earth twenty-one times over, and filled five lakes with their blood. Ultimately, his grandfather, the great rishi Rucheeka, appeared and made him halt. He is a Chiranjivi, and believed to be alive today in penance at Mahendragiri.
Rama: Ramachandra, the prince and king of Ayodhya, appeared in the Treta Yuga. Rama is a commonly worshiped avatar in Hinduism, and is thought of as the ideal heroic man. His story is recounted in one of the most widely read scriptures of Hinduism, the Ramayana. While in exile from his own kingdom with his brother Lakshman and the monkey king Hanuman, his wife Sita was abducted by the demon king of Lanka, Ravana. He travelled to Ashoka Vatika in Lanka, killed the demon king and saved Sita.
Shree Ram is not called Purna Avtar. Only Krishna Avtar is Purnavatara… Rama was 14 kala sampurna and krishna was 16 kala sampurna. This is because of a boon to Ravana. He was promised that no God would kill him. So Rama intentionally hid his 2 kalas and behaved like a common man (to fulfil the boon that Ravan would be killed by a man). This answers why Rama cried for his wife and the reason for taking help from monkeys.
Krishna: was the eighth son of Devaki and Vasudev. Krishna is the most commonly worshiped deity in Hinduism and an avatar in Vaishnava belief. His name means ‘dark’ or ‘attractive’, and he appeared in the Dwapara Yuga alongside his brother Balarama, and was the central character of the Bhagavad Gita, the most published Hindu canon. He is mentor to Arjuna, delivering him the Gita at the Battle of Kurukshetra. He is often depicted playing the murali, (flute), and having a mischievous spirit. The appearance of Krishna coincided with the beginning of Kali Yuga.
Krishna Avatara alone is considered as Poorna Avatara: 16 kalas: 1) Anna Maya 2) Pranamaya 3) Mano Maya 4) Vigyanamaya 5) Anandamaya 6) Atishayini 7) Viparinabhini 8) Sankramini 9) Prabhavi 10) Kunthini 11) Vikasini 12) Maryadini 13) Sanhaladini 14) Ahladini 15) Paripurna 16) Swarupavasthitha
Rama is avatar but he didn’t know that till Lord Yama reminded him of it at the end of his life and he behaved like a human being who respects parents and their decisions. He carried out his duties as a normal human being. But in the case of Lord Krishna he knew that he is Vishnu’s avatar and behaved like that and delivered the Gita to Arjun at the battle field