"What group of people are preaching that message in “all the nations”? The answer is obvious—only Jehovah’s Witnesses". Watchtower May 16 2016
I looked into this awhile back and the United Bible Society are doing way more preaching in more languages :
From Wikipedia, they surpass WTBTS by far :
See also: International Bible Society, Wycliffe Bible Translators, and Institute for Bible Translation
The Bible is the most translated book in the world. The United Bible Societies announced that as of 31 December 2007 the complete Bible was available in 438 languages, 123 of which included the deuterocanonical material as well as the Tanakh and New Testament. Either the Tanakh or the New Testament was available in an additional 1,168 languages. In 1999, Wycliffe Bible Translators announced Vision 2025—a project that intends to commence Bible translation in every remaining language community by 2025. They currently estimate that around 209 million people, representing 2.95% of the world's population, speak those 1,967 languages where translation work still needs to begin. In November 2012, Wycliffe stated that parts of the Bible are available in 2,798 languages out of the 6,877 known languages, and that there are currently 518 languages with a complete Bible translation. At least 5 billion people (71% of the world's population) have access to a full Bible translation in their native language. Wycliffe added that a further 595 million (8.5% of the world's population), representing 1,275 languages, have at least the New Testament in their first language. An additional 1,005 languages (almost 20% of the world's population) were reported to have at least one book of the Bible available. By September 2012, personnel from participating Bible translation organizations were involved in 2,075 language programs.