The statement that correctly compares the involvement in the Vietnam War during different presidencies is:
The number of troops at the end of Nixon's presidency was less than the number of troops at the beginning of his presidency.
During Nixon's presidency, there was a process of "Vietnamization," which aimed to reduce U.S. troop levels in Vietnam, resulting in a decrease in American military presence by the end of his term compared to the beginning. The other statements are inaccurate regarding the troop levels during the presidencies of Eisenhower, Kennedy, Johnson, and Nixon.