Q: Are Krishna and Christ the same?
A: This is a good question. It is one that is often assumed by many—that Krishna and Christ are the same. It is also a question that is asked by many people, so I will give a lengthier answer to try to make things clear. The way to answer this question is to see: 1) does one or the other claim to be equivalent? 2) do what they agree with one another?
To the first point, there is a simple and straight answer: no. There is no claim of Christ to be Krishna in the New Testament. As well, there is no claim of Krishna to be Jesus of the New Testament.
The second point is a little more difficult to answer. However, it is the more important point to give an answer to, as the absence of a claim from either to be equivalent does not prove they are not the same, only that they left the subject quiet and perhaps to cast some doubt upon their equivalence. If they are the same, then we would expect very definitively to find that the teaching of each would not contradict one another and would show at least a basic agreement, certainly not disagreement with one another.
There are few points in which there might be some grounds of agreement. First there is the claim to be divine. Jesus makes this claim very clearly and openly. The following is a small sampling of some of the examples of this from the New Testament:
John 1:1 In the beginning was the Word, and the Word was with God, and the Word was God (This passage identifies Jesus as the word, equivalent to God)
John 10:30 I and the Father are one.
John 14:7 If you really knew me you would know my Father as well. From now on, you do know Him and have seen Him.
John 14:8-9 Philip said, “Lord, show us the Father and that will be enough for us.” Jesus answered, “Don’t you know me, Philip, even after I have been among you such a long time? Anyone who has seen me has seen the Father.
John 5:18 For this reason the Jews tried all the harder to kill him; not only was he breaking the Sabbath, but he was even calling God his own father, making himself equal with God.
Colossians 2:9 For in Christ all the fullness of the Deity lives in bodily form
Heb 1:3 The Son is the radiance of God’s glory and the exact representation of His being, sustaining all things by his powerful word.

When we look at Krishna, there are also claims to divinity. Let me give a few that should suffice:
1. [Thus] I too penetrate the earth and so sustain [all] beings with my strength….I dwell in the body of all that breathes; conjoined with the inward and outward breaths, I digest the fourfold food. I make my dwelling in the hearts of all: from me stem memory, wisdom refuting [doubt]. Through all the Vedas it is I that should be known, For the Maker of the Veda’s end am I, and I the Vedas know. (Hindu Scriptures, The B.G., XV,13-15. Goodall, Dominic)
2. Bear Me in mind love Me and worship Me, sacrifice, prostrate thyself to Me; So shalt thou come to Me, I promise thee… (Ibid., XVIII, 65)
3. By Me, Inmanifest in form, This whole universe was spun; In Me subsists all being… (Ibid. IX, 4)

These claims are somewhat similar in that they are claims to either be divine, or they are claims to attributes that belong to divinity. In the thinking of Hinduism, there is a general practice of incorporating other gods into the Hindu system. In practice, Jesus is often worshipped by Hindus alongside the usual Hindu gods. This of course then would lead to the possibility of stating that Krishna and Christ are the same. Hinduism teaches the familiar concept that “all roads lead to God.” So from the side of Hinduism, this would certainly promote the possibility of viewing Jesus as another incarnation of god, or of possibly seeing Jesus and Krishna as the same. But let us investigate further. The claim to divinity is not enough to determine that they are the same. There have been multiple claims to divinity. The test for sameness is if their teaching and words can match. If they do, this would lead one to seriously consider their being the same a possibility, in spite of the lack of claims to this end. If their teaching does not match, then all hope of their being the same essentially vanishes.
Let me Upon further investigation of the content of their teaching, the apparent similarity quickly vanishes. If you put the teaching of Jesus on topics next to the teachings of Krishna on the same topic, you find not similarity, but difference. Let me demonstrate this through the following topics of their teaching: the nature of the soul of man, the nature of evil and good, the problem of evil, and the nature of salvation.

First, the nature of the soul. Krishna teaches in the Bhagavad-Gita that the soul passes from one life and one body to another (“Just as in this body the embodied soul Must pas through childhood, youth, and age, So too [at death] will he take another body up” (Hindu Scriptures II, 13. Goodall. See also verse 22)). In contrast, in the New Testament, the disciples of Jesus taught that men are “Destined to die once, and after that to face judgment.” (Heb 9:27).

We also find a striking contrast as in the teaching of Krishna in non-dualism, where with Jesus we find strong statements of evil and good and exhortations to recognize the differences and embrace the good. A few examples of the teaching of Krishna first:
Whoever is integrated by [the yoga of] the soul Discards both good and evil works; (Hindu Scriptures, II, 50. Goodall)
Who has no love for any thing, who rejoices not at whatever good befalls him, not hates the bad that comes his way (Ibid. II 58)
In contrast to this stands the teaching of Jesus, to love and embrace with discernment those things which are good, right and just, and to reject their opposites:
Love your enemies (Matthew 5:44)
Love your neighbor (Matthew 19:19)
Put to death, therefore, whatever belongs to your earthly nature: sexual
immorality, impurity, lust, evil desires and greed, which is idolatry. (Colossians
3:5)
Finally, brothers, whatever is true, whatever is noble, whatever is right, whatever
is pure, whatever is lovely, whatever is admirable— if anything is excellent or
praiseworthy— think about such things. (Philippians 4:8)
These statements show clearly that there is a form of desire and attachment that Jesus strongly recommends. This is one of the very clear teachings of His throughout the New Testament. In contrast, Krishna teaches attachment and desire is the source of man’s problems, it is in the very nature of the issue of his problem. The very categories of good and evil are abandoned in his teaching in favor of a pure detachment.

We also find the reason for the trouble of man is strikingly different. Krishna
teaches man is destroyed from attachment. He teaches that his senses are seductive
and pursuing detachment is man’s hope. He links this problem as follows: from
attachment comes desire, from desire comes anger, from anger comes bewilderment,
from this comes the destruction of the soul (cf. B.G. II, 62-63). In contrast to this, Jesus
denies that attachment or desire is the problem. It is not desire itself (both good and
evil) , but something within the heart of man that produces evil desires that is the
problem. “Therefore do not let sin reign in your mortal body so that you obey its evil
desires.” (Romans 6:12). Jesus said, “But the things that come out of the mouth come
from the heart, and these make a man ‘unclean.’ For out of the heart come evil
thoughts, murder, adultery, sexual immorality, theft, false testimony, slander. These are
what make a man ‘unclean’.” (Matthew 15:18-20).

Lastly, from these ideas flow the strong contrast in teachings on the salvation of the soul. For Krishna it is detachment that brings one salvation. The means is yoga and meditation on Him. For Jesus, it is the forgiveness of sins from God that brings one salvation. The means is provided by Jesus taking the punishment of our sins in his body on the cross.

This short survey of the teachings of Jesus and the teachings of Krishna show that in such essential issues the nature of the soul of man, the nature of evil and good, the problem of evil, and the nature of salvation there are striking differences. Indeed, there are completely different and contradictory thoughts about these foundational ideas. This makes any possible similarity between the two vanish.