In the Srimad-Bhagvatam, Lord Buddha is accepted as a saktyavesa avatara, a specially empowered incarnation of the Supreme Lord. Srimad-Bhagvatam, which was compiled by Vyasadeva five thousand years ago, foretold the incarnation of Lord Buddha who appeared just 2,600 years ago, saying Buddha will appear in Gaya Pradesh, in the province of Gaya. "In the beginning of Kali-yuga, the Lord will appear as Lord Buddha, the son of Anjana, in the province of Gaya, just for the purpose of deluding those who are envious of the faithful theist." (Srimad-Bhagavatam 1:3:24). Kesava dhrta buddha sarira - Krsna has accepted the body of Buddha. That is the Vaisnava conception of Lord Buddha.
Lord Buddha appeared at a time when the so-called religionists were falsely using the Vedas to justify violent acts like meat-eating and animal sacrifice. It was the desire of the Supreme Personality of Godhead to end violence being committed in the name of the Vedas. Taking compassion on the poor animals, he appeared as Lord Buddha to preach ahimsa, non-violence, leading the fallen people away from such false interpretations.
At the time of Lord Buddha's appearance, many people had become atheistic, and Srimad-Bhagvatam states that Lord Buddha appeared in order to bewilder this atheistic class of men. Due to their ignorance, the people were being implicated in innumerable sinful activities by unnecessary animal killing in the name of religion. In his preaching, Lord Buddha declined to accept the Vedic principles because the animal-killers would have simply pointed to evidences that in the Vedas there is mention of animal-killing for sacrifice. Therefore, Lord Buddha established a system of religion on the platform of non-violence to stop the nonsense they were engaging in due to a lack of knowledge.
Lord Buddha preached atheism so that the atheists would follow him and thus be tricked into devotional service to Lord Buddha (Krsna). By obeying Lord Buddha, they were actually following God. In order to take the bewildered atheists under his control, he collaborated and said, "Yes, there is no God, but you hear me." Being an actual incarnation of God, this was a kind of transcendental cheating. Those who were followers of Vedic religion, however, did not accept Lord Buddha's religion because it was against the Vedas. In other words, this philosophy is actually meant for bewildering the atheists and should not be accepted by devotees.
Lord Buddha was criticized by the Vedic brahmanas for stopping animal sacrifice, which is recommended in the Vedas as a means of creating new life under very special circumstances. But because the brahmanas had become corrupted and were taking this injunction as a very general thing, Lord Buddha refused to accept the Vedic principles and instead criticized them. Consequently, strict followers of the Vedas would not accept him. The devotee understands why Lord Buddha took this position, however, and while a devotee does not accept the philosophy of Buddhism, he accepts Lord Buddha as incarnation of Lord Krsna and offers obeisances to him. This is the Vaisnava position.
Buddhism spread during the reign of Emperor Asoka, a Hindu king. Lord Buddha, who appeared in the family of a high-grade ksatriya king, was patronized by Maharaja Asoka and Buddhist philosophy was consequently broadcast across the Far East. After the great teacher Sankaracarya soundly defeated the philosophy, Buddhism was driven out beyond the borders of India, and Jainism and similar religious principles became more visible. Eventually, Buddhism all but disappeared in India, taking root instead in China, Burma and Japan where it remains a predominant religion.
The Buddhist philosophy does not accept the existence of God or the soul. Consequently there is no possibility of bhakti-yoga, because they do not recognize the Supreme Lord existing as the supreme objective. While Buddhists do not believe in God they do have love for Lord Buddha, so love is there. Some Buddhists say that because they show devotional service to Lord Buddha, they should be considered devotees, but the Vedas do not accept as a devotee one who does not reach the conclusion of the supremacy of the Personality of Godhead. In essence, Buddhists simply philosophize on the material elements, and want to dismantle the material elements by the process of reaching Nirvana. Even those personalities like Lord Buddha, who did not accept the existence of Godhead and preached morality and ethics in the spirit of atheism, never preach that there is any possibility of attaining eternal peace and prosperity in this material world.
"Buddhism is concerned largely with the predicament of the body. Due to the interactions of the three modes of material nature, which are acting on our material bodies, we experience various pains and pleasures. Buddhism teaches that one can be relieved of these pains and pleasures as soon as one dismantles the combination of the material elements in the shape of the physical body. Nirvana, the goal of Buddhism, is the state attained when a person has finished with the material combinations. After all, pains and pleasures are due to possessing this material body. However, Buddhist philosophy does not provide information about the soul, the possessor of the body. Thus Buddhism is imperfect.
Buddhist philosophy is incomplete, but that does not mean Lord Buddha did not know the complete truth. A teacher may have received his Masters degree, yet he still teaches the ABC's to his students. It is not that his knowledge is limited to the ABC's. Similarly, any especially empowered incarnation (saktyavesa avatara) will preach God consciousness according to time, place, and circumstances. The teacher holds his Masters degree, but the students may not be qualified to receive the high instructions that the teacher is competent to teach.
Therefore there are different schools of religion, like Buddhism and Sankaracarya's Mayavada philosophy. Both the Buddhists and the Mayavadis encourage their followers to try to get free of pain and pleasure, which are due to sensual activities. No genuine philosopher urges his followers to pursue sensual activities. Buddha finishes with matter: to achieve nirvana one must first dismantle the material combination of the body. In other words, the body is a combination of five material elements: earth, water, fire, air, and ether, and this combination is the cause of all pain and pleasure; so when the combination is at last dismantled, there will be no more pain and pleasure."
Second Chance, Chapter 11
"It is stated that mercy is one of the qualities of a Buddhist, but mercy is a relative thing. We show our mercy to a subordinate or to one who is suffering more than ourselves. However, if there is a superior person present, the superior person cannot be the object of our mercy. Rather, we are objects for the mercy of the superior person. Therefore showing compassion and mercy is a relative activity. It is not the Absolute Truth. Apart from this, we also must know what actual mercy is. To give a sick man something forbidden for him to eat is not mercy. Rather, it is cruelty. Unless we know what mercy really is, we may create an undesirable situation. If we wish to show real mercy, we will preach Krsna consciousness in order to revive the lost consciousness of human beings, the living entity's original consciousness. Since the Buddhist philosophy does not admit the existence of the spirit soul, the so-called mercy of the Buddhists is defective."
Caitanya-caritamrta, Madyam lila 9:49
Bhaktivedanta Book Trust. Excerpted from text and purports of HDG A.C. Bhaktivedanta Swami Srila Prabhupada.