There seem to be many variations of the text of HaNeros Hallalu, the explanatory paragraph that people recite while lighting Hanukkah lights. Is it possible to list the major versions? What are the issues that make people prefer particular versions?
A great article on this topic is by Rabbi Daniel Sperber in Minhagei Yisrael, Book 5 Chapter 2. It addresses your question (some of it directly, otherwise, by the sources he cites) and much of it is available within the 40 page viewing limit on Otzar Hachochma (page 27 in their pdf here). Another useful resource (albeit much shorter) is the Wikipedia page for Haneiros Halalu. Images are taken from Minhagei Yisrael.
In short, there are a number of versions (seen in both links above).
The Maharshal has one version (also cited by the Tur much earlier from Maharam Mirotenberg), and he suggests that there should be 38 words (Haneiros Halalu + 36 more, meant to represent the 36 Chanukah candles we light, not including the Shamash). Except that his version has 41 words in total (Haneiros Halalu + 39):
Various Mefarshim deal with this in different ways, see the article for the suggestions of the Mateh Moshe and Elyah Rabbah.
There is a version attributed to the Rosh by the Mateh Moshe, which adds words to the version above until it reaches 44 total words (Haneiros Halalu are included in that count), except that all of the other sources that mention the Rosh say that his had 41 words as well, with one small change within.
Although the Tur quoted the version that he had ("Maharshal's version") from the Maharam Mirotenberg, our version of the Maharam Mirotenberg's teshuvos have a 38 word total (Haneiros Halalu + 36).
All of these versions are based on the original in Maseches Sofrim 20:7 (20:4 in some versions), but clearly, we had different versions of that at different times, so that's what the disagreements are based off. The version of Maseches Sofrim that we have now is no more authoritative than what the Rishonim had. In determining a correct text, some will also potentially take the number of words into play.
- Haneiros Halalu...
- Vechol Shmonas Yemei Hachanukah...
- Kedei Lehodos...
He reconstructs a "Nusach Mekori", which is remarkably different than what we have, but see the R' Sperber article in Minhagei Yisrael or Goldschmidt's book for details.
For Sam: Rabbi Sperber notes that none of the Rambam's, Rif's, or Rashi's followers (including Machzor Vitri), as well as many, many others (prior to the Maharm Mirotenberg) mention the Minhag to say this.