What were the objectives of the Gospels of Buddha and Jesus the Christ?
The question makes more sense to me if the word "objects" is replaced by "objectives". So I will answer the question question as such.
The objectives of the Buddha and Lord Jesus Christ, Lord of lords and King of kings are vastly different.
The objective of Gautama Siddhartha was to avoid suffering and eventually snuff desire.
The Buddha believed that desire brought pain. Wherever he looked, he saw the misery of people, the misery of suffering; he saw those who refused to work and who desired evil. He believed that within himself, he suffered because of his desires. The Buddha's conclusion was that desire was the cause of suffering.
The Buddha then based his philosophy of salvation around avoiding suffering by alleviating desire. To this extent, he developed what are termed "The Four Noble Truths". These are:
1. the truth of suffering
2. the truth of desire
3. the truth of desire’s cessation
4. the truth of the eight-fold plan
The eight-fold plan is a means by which the practitioner can survive existence on Earth while seeking to avoid suffering by squelching inner desires. The objective is to eventually become free of desire through meditation. Once desire is subdued then it is believed nirvana can be attained, and when one dies, one goes back into mindlessness and non-existence.
Contrasted to this the objectives of Lord Jesus Christ (the pre-existent Son of God through Whom all things were made) in coming to Earth were:
to prove that God is righteous
to live without sin
to become the ransom for mankind
to leave an inheritance
Nobody asked to be born to suffer and then die, therefore God had to make a way out for everybody. To do this, the pre-existence Son of God, the Living Word of God, became flesh and lived a live without sin, and permitted the Evil One to take His life on the Cross of Calvary. In doing this, Jesus become the ransom for the life of the first man Adam who lost authority over the Earth when he sinned against God and subjected himself to the Evil One. Because Jesus died and had not sinned, He left His life as an inheritance for every person who is alive from that time on to claim. Jesus accomplished those four objectives and demonstrated He was the Author of Life, by rising from the dead.
However, the main objective is for us to receive the guarantee of our inheritance, and this Lord Jesus provides, by baptizing people with the Holy Spirit. When this happens, unlike opinionated fools, we would expect to have obtained something that would be worth talking about.
The word "gospel" means good news.
The good news according to the Buddha is "if you struggle to overcome your desires and succeed, you will attain mindlessness, a state of non-being in the next life. But there is no guarantee."
The good news according to Lord Jesus Christ: "I have paid the price for sin and I have left you an inheritance, of which I will give you a guarantee, once you have claimed it."
When we consider the two claims, one has no guarantee and the other has a guarantee, what does this tell us. One sounds like bad news and one sounds like good news.
I possess the guarantee of the my inheritance. So I know what I am talking about.
If we were to compare the concept of a guarantee with having money in the bank and not having money in the bank, we get the idea of who are fools and who are wise.
Which of the two is truly a gospel of good news? The message to struggle in life to attain something that the founder did not attain. Or the message to seek the guarantee of eternal life and receive the baptism of the Holy Spirit by calling upon the name of Lord Jesus Christ who rose from the dead after paying the price for your sins.