How does the tone contrast between the two essays?

The first essay of The Fire Next Time is addressed to the author's nephew, on the occasion of the 100th anniversary of the Emancipation Proclamation. Baldwin's purpose is to give the young man an assessment of the situation in the US as it exists, in which, despite all the time that has passed since the Civil War, so much is still wrong. Baldwin writes to his nephew in the tone of one man to another who already has at least an intuitive grasp of the facts, as all African Americans do, but may still lack the maturity to have a complete understanding of them. His purpose is to articulate, as a writer such as himself would best be able to do, an objective view of the racial divide and also to impart some feeling of hope to the young man, no matter how dark the situation may appear.
The second essay is addressed to world at large, including people who, even if they are progressive in their thinking, may still not have much understanding of the African American perspective. It is partly a denunciation of a racist society which at that time had just begun to be challenged by the Civil Rights movement, then still in its infancy. But it is also an attempt to correct misconceptions and blind spots that white people, even liberals, still have about the history of racial oppression in the US and about the bigotry still endemic in American society. At the same time, Baldwin is addressing the African American community and those within it, such as Elijah Mohammed's Nation of Islam, who, in Baldwin's opinion, are seeking unrealistic solutions to the problems of racism and oppression.
It would be a bit simplistic, but partly correct, to state that the chief difference in tone between the two essays is that the first is much milder and more positive. The second essay is essentially a direct and uncompromising warning to America that something must be done, and soon, to change the overall situation, lest the prophesy come true in the words,

God gave Noah the rainbow sign,
No more water, the fire next time!