The Letter has been published in several different places, though usually not in full.
The complete Letter is said to be over 10,000 words long. It has been published in the following seven places:
The Letters of J.R.R. Tolkien (1981)
Includes around 75% of the text, omitting a summary of The Lord of the Rings.
Sauron Defeated (1992)
Includes the ending of the previously omitted LotR summary, covering just the Scouring and the Epilogue.
The Silmarillion - second edition (1999)
Includes the first 60% of the letter, omitting the Third Age portion, the LotR summary, and the conclusion.
Conference #12, "Lettre a Milton Waldman: L'horizon de la Terre du Milieu" (2001)
Includes the full text, but translated into French.
La Feuille de la Compagnie 2: Tolkien, les racines du légendaire (2003)
Includes the full text in both English and French.
The Lord of the Rings: A Reader's Companion (2005)
Includes around 25% of the text, basically just the LotR summary but with a few of the surrounding paragraphs.
Tolkien Estate Website (2015)
Includes three extracts, adding up to around 20% of the text.
Other than the new preface, the only changes are a few typo corrections, and the change of numbering of the Numenorean kings.
At the end of his preface, right before the letter extract, Christopher talks about the other changes made:
I have removed a number of errors in the text and index which until now
have escaped correction in the hardback printings (only) of The Silmarillion.
The Silmarillion - "Preface to the Second Edition"
James Tauber, in his project to analyze the textual variants of different Silmarillion editions, has identified these changes as follows:
- Chapter 20: For there all the Noldor of Hithlum were asssembled [> assembled], together with Elves of the Falas and Gwindor's company from Nargothrond
- Chapter 24: Then Eärendil, first of living Men, landed on the immortal shores; and he spoke there to Elwing and to those that were with him, and they were three mariners who had sailed all the seas besides [> beside] him: Falathar, Erellont, and Aerandir were their names.
- Akallabêth: And the nineteenth [> twentieth] king took the sceptre of his fathers, and he ascended the throne in the name of Adûnakhôr, Lord of the West, forsaking the Elven-tongues and forbidding their use in his hearing.
- Akallabêth: The mightiest and proudest was Ar-Pharazôn the Golden of all those that had wielded the Sceptre of the Sea-Kings since the foundation of Númenor; and three [> four] and twenty Kings and Queens had ruled the Númenóreans before, and slept now in their deep tombs under the mount of Meneltarma, lying upon beds of gold.
- Akallabêth: But he that is their master shall yet prevail, and he will deliver you from this phantom; and his name is Melkor, Lord of All, Giver of Freedom, and he shall make you stronger then [> than] they.
Three of these changes are just typos, and are not the only ones to have been fixed in new printings of the book since its original release. The other two however are more significant, and reflect a change in Christopher's understanding of the text.
Chief among these are those that concern the numbering in sequence of certain
of the rulers of Númenor (for these errors and an explanation of how they arose
see Unfinished Tales (1980), p.226, note 11, and The Peoples of Middle-earth (1996), p.154, §31).
The Silmarillion - "Preface to the Second Edition"
The gist of what happened is that Appendix A of The Lord of the Rings gives a list of Númenórean rulers in which Ar-Adûnakhôr is the nineteenth on the list, but then also refers to him in the text as the twentieth ruler. Christopher assumed the list was correct but the number a mistake, and so when editing the Akallabêth to include in the Silmarillion, also changed the number there from 20 to 19. Later he found the text "The Line of Elros" (published in Unfinished Tales, which has an additional name on the list, showing that he really was the twentieth king, and so undid his correction. More information can be found in the sources Christopher refers to, as well as in James Tauber's excellent write-up "Numbering in the Númenórean King Lists".