If Gautama Buddha had been with Arjuna in place of Lord Krishna during the battle of Kurukshetra in the Mahabharata, would he have advised Arjuna? What was the war then?

First we memorize a verse from the Srimad Bhagavat Geeta

यदा यदा हि धर्मस्य ग्लानिर्भवति भारत |
अभ्युत्थानमधर्मस्य तदात्मानं सृजाम्यहम् || 7||

परित्राणाय साधूनां विनाशाय च दुष्कृताम् |
धर्मसंस्थापनार्थाय सम्भवामि युगे युगे || 8||

BG 4.7: Whenever there is a decline in righteousness and an increase in unrighteousness, O Arjun, at that time I manifest myself on earth.

BG 4.8: To protect the righteous, to annihilate the wicked, and to reestablish the principles of dharma I appear on this earth, age after age.

        God never confirmed the number of his incarnations. But according to the Puranas, a list of 64 incarnations, 39 incarnations and 24 incarnations has been made. But his list of 10 avatars is the most popular. Because in these 10 incarnations, just as evolution has been shown, so has the social system at different times.

These 10 incarnations are -

"Matsya, Kurma, Varaha, Narsingh, Baman, Parashuram, Rama, Balarama, Krishna and Kalki". This is the oldest list of the top 10 avatars. In some lists, "Krishna is the eighth and Gautam Buddha is the ninth" incarnation.

          

Now look at its similarity with evolution, "The first aquatic creature in the world originated, then the first incarnation of God was the fish. Then some animals came ashore and amphibians originated. Then the terrestrial creature originated, so the third incarnation was the pig. Then the monkey race originated which was like many human beings, so the fourth incarnation of God is the lion. "

          Then "the first human race in the world was born who was physically short, so the fifth incarnation of God was a dwarf. Then man learns to hunt so the people of that time were very violent nature, the sixth incarnation is Parshuram. From then on came social people, Rama, Krishna, Buddha". 

Note that the incarnations of Varaha and Narasimha preceded the incarnation of Kurmo, but the incarnation of Kurma came second to show evolution.

           Then came the social system, in the true age no one had any sin in mind, everyone was pious and lived a peaceful life, there were only a few demons in the list of unrighteous. The society was like this till the early part of the Treta era, so the incarnations of this period are temporary, Matsya, Kurma, Varaha, Narsingha, Dwarf. Then in the middle of the Treta era the kings became very arrogant and they became oppressors, then Parshuram came down to destroy the arrogance of those Kshatriya nations. Who eradicated Kshatriya from the earth 21 times and destroyed the arrogance of all the kings. But due to the eviction of so many Kshatriyas, many states suffer from anarchy, which leads to theft and robbery all around. Strict law and order is required to curb this lawlessness, so different constitutions are made. This time when the dignity is established, the dignity will be the best of men, then Lord Rama incarnated, the incarnation at the top of all the dignity. The last incarnation of the Treta era. Then in the age of Dwapar it is seen that iniquity can be committed even within the rules. When such a situation arises when the rules have to be changed, Lord Krishna descends towards the end of the day. Who breaks dignity and establishes dignity and changes society. He explains that "what you do is not important, the reason behind it is important." Then the Kali Yuga begins and when the influence of Kali brings sorrow to people's lives, then God descends in the form of Buddha to show them the way. Now Kali Yuga is going on and in this Kali Yuga there is no end to human misery, sin and lawlessness all around. It is said that he did not have the opportunity to commit any sin in this abyss. In other words, there is some or the other stigma in everyone's life, so at the end of the Kali age, God will incarnate as Kalki, which will be completely spotless. God will end the Kali Yuga in this Kalki incarnation and establish the Satya Yuga.

           That is, God sees the situation and does the leela, when he needs to do or get it done, then he does or gets it done. So if there was a Buddha in the place of Lord Krishna, it would be just a difference of name, the work would be the same.