What is the toughest mission to serve in for The Church of Jesus Christ of Latter-day Saints?
A lot depends on how you define "tough."
However, if you define it as how many average converts a missionary baptizes during his/her mission, then I'd peg my mission, England-Bristol, as thee toughest, and at the least one of the toughest of all.
In fact, I'd put ALL of Europe in the toughest in the world category.
I'd estimate the average missionary in the U.K. or Europe only baptizes a few or a handful of converts in two years of service.
Furthermore, England Bristol doesn't even exist as a mission anymore.
Whereas in Central and South America in particular, missions have been divided and multiplied many times over the decades, there are actually LESS missions in the United Kingdom today than in the 1970s.
Missionaries were also "chewed out" in the early 1990s by a regional leader for their low baptism numbers. Eleven years later, in 2002, the mission was disbanded and merged with two adjoining missions.
(In addition to being tough for converts, this mission is also among the most expensive in all the world -- though costs missionaries pay are equalized world-wide, except for couples.)
--ALL of Europe is in a steep religious decline overall.
In fact, the England Bristol Mission ceased to exist on July 1, 2002, after some 40 years of existence. The England London mission gained part of the former Bristol mission and the England Birmingham mission received the rest.
Where else in the world are you going to find LESS missions in existence and likely less full-time missionaries serving, except in the United Kingdom and Europe?
The "why" this may be so is another story.