The most famous debate between a Mormon and non-Mormon preacher

The Deseret News announcement of a debate over polygamy between Orson Pratt and President Ulysses Grant’s personal pastor.

And this summary from the Wardell Family Genealogy site:

In August, 1870, Dr. John P. Newman, chaplain of the U.S. Senate and President Ulysses S. Grant's personal pastor, delivered a strong anti-pologamy sermon in his Metropolitan Methodist Church in Washington, D.C.

Salt Lake Daily Telegraph editor Edward Sloan proposed that Newman debate polygamy in Salt Lake.

Newman accepted and, when Brigham Young declined to be his opponent, debated instead with Orson Pratt.

The 3 day debate was reported daily in the New York Herald. Edward Tullidge declared that "millions of readers followed the arguments of Dr. Newman and Orson Pratt and it is safe to estimate that quite two-thirds of them yielded to the Mormon apostle. It is reported that Newman never forgave "the Mormons". 

- http://wardell-family.org/bates/not15.htm

And this from

Salt Lake City l9 January 1871
Elder P. O. Thomassen

Dear Brother,
Thank you for your letter of 20 December. Since returning from my mission in Denmark I have had some amusing experiences, including a few religious ones. I'll try to tell you a little about them.

First, the "learned" chaplain of the American Congress, Dr. Newman, challenged our president to a debate on the frequently discussed question, "Does the Bible sanction polygamy?"

Brigham Young found it beneath his dignity to defend our principle, but sent Orson Pratt in his stead.

The debate lasted three days.

The first two Elder Pratt lathered his learned opponent, and the third he shaved him as smooth as an eel.

I attended the entire debate. Shortly afterward several American newspapers, both in California and the eastern states, wrote things like: "The learned Reverend Dr. Newman recently went to 'the city of the Saints' to convince both the prophet and all true Mormons that polygamy is wrong. He wanted to point out verses in the Bible that forbid its practice.

Old Brigham did not himself refute Dr. Newman, but sent one of his apostles, Orson Pratt, who did it so impressively that we must tell the learned gentleman from Washington the same thing the Savior told the woman: 'Go and sin no more."

- Letters: Scandinavian Saints write about America