The letter is available in The Letters of JRR Tolkien where it's published as Letter #131.
Both the second edition Silmarillion and Letters omit an extended passage which is a summary account of events in Lord of the Rings. This passage is published in Hammond & Scull's Readers Companion.
The Silmarillion version furthermore ends a little earlier than the Letters version, finishing at the end of the Second Age with the sentence:
So ends the Second Age with the coming of the Númenórean realms and the passing of the last kingship of the High Elves.
In Letters the text continues with an account of the Third Age (omitting the LotR summary) and a concluding argument for publication of LotR and The Silmarillion together (which at the time Tolkien greatly wished - that indeed was the purpose of the letter in the first place):
If the other material, 'The Silmarillion' and some other tales or links such as The Downfall of Númenor are published or in process of this, then much explanation of background, and especially that found in the Council of Elrond (Bk II) could be dispensed with. But altogether it would hardly amount to the excision of a single long chapter (out of about 72).
I wonder if (even if legible) you will ever read this ??
The second edition contains no other appreciable differences to the first; quoting from Christopher Tolkien's foreword:
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.
There is therefore nothing particularly "new" about this edition, and if you already have the material elsewhere (i.e you have Letters and you don't have a hardback copy), you've already got everything in it.