Re: What is the biggest fight in boxing history?
Now that the last century is solidly behind us, only one fight carries the acronym "FOTC," and it's not Louis-Schmeling II. During the build-up, it was simply called, "The Fight."
Louis-Schmeling II was obviously huge, and the passing of Louis led off the nationally broadcast news reports primarily on the basis of it. (I believe that was the last time the death of a boxing champion led mainstream news coverage, something not likely to happen again until the passing of Ali.) Louis himself did not want to be addressed as champion until defeating Schmeling, and may have always privately considered this the true beginning of his landmark reign.
After those bouts, it depends on whether you're referring to significance before and during, or after the fact. I'll toss out some other matches for consideration here.
Tunney-Dempsey I & II
Fitzsimmons-Corbett. This one was important enough for Enoch Rector to film on location, allowing everybody an opportunity to see the same competitive bout for the first time, not just read about it.
Holmes-Ali. This may have actually been the biggest boxing event in world history, as it was broadcast live to the U.S.S.R. and People's Republic of China. Ali was far bigger than John Lennon ever imagined the Beatles to be, as Red China's state controlled media only acknowledged the existence of the Beatles for the first time when he was murdered (a couple months after Holmes-Ali). The Beatles (and rock music in general) were outlawed in the other Communist states. Ali is infinitely more transcendent.
Duran-Leonard I. The biggest non heavyweight fight of my lifetime. Many believed that the larger and younger SRL was the P4P best in the world at the time. Duran leapfrogged the junior welterweight class to cement his all time P4P status.
Dempsey-Willard, after the fact. At the end of the century, a prominent sports magazine (Sports Illustrated?) ran down their list of the most important of the last 100 years in sports. 1919 was at the top of that list, primarily on the basis of the sensational impact of Dempsey's dethroning of Willard.
Ali-Foreman. The outcome of this one brought the HW Title out of mothballs. Muhammad was a great fighting champion, putting the title up five times in 1966, and twice before April of 1967. After dethroning Big George, he put it up for grabs four times in 1975, and four more times in 1976.