This is one of those cool, rare finds. We dug through the 1920 U.S. Census and found the two men who would eventually face off in the 1960 United States presidential election.
First, let’s take a look at the two when they were boys.
Now, the first census below shows the Nixon family in the 1920 U.S. Census, including father Francis Nixon, mother Hannah Milhous Nixon, and four sons: Harold, Richard, Francis Donald, and Arthur. A fifth son, Edward, was born in 1930. The census was taken on January 6th, 1920 in Placentia, California.

Source: Ancestry.com
Below is a close-up of his record. Click the above image for the full page.

And here is the 1920 U.S. Census showing the Kennedy family of Massachusetts.

Source: Ancestry.com
And, below is a closer look at JFK in the census.