Galadriel's

[Galin]

Originally Posted by The Might

Still, I think all in all the change wouldn't have been that great. Galadriel does seem to appear as more of a teacher than a ruler coming to M-e, but surely Tolkien never intended to also change the text in LotR. So perhaps her desire to rule wouldn't be so clear within the Silmarillion, but would develop until the time of LotR.

In my opinion, in general it would be a quite notable change concerning a major character, but I think you mean in the context of the actual expression of Galadriel's motives to seek Middle-earth, and in that narrowed sense -- and with respect to the Silmarillion tradition proper, or even including the Annals -- there's not much text to alter if I remember correctly.

The Later Quenta Silmarillion (phase I in the early 1950s) noted that (after the oath of Feanor): '... for Angrod and Egnor and Galadriel were with Fingon, whereas Orodreth stood aside and spoke not.' It is in The Annals of Aman that Galadriel is said to have yearned to see the wide untrodden lands '... and to rule there a realm maybe at her own will'. Tolkien seems to further 'explain' this by adding that she was the youngest of the House of Finwe, and came into the world west of the Sea '... and knew yet nought of the unguarded lands.'*

In The Grey Annals Galadriel tells Melian that the Noldor came of their own will, and against that of the Valar, and: 'For this purpose we came: to take vengeance upon Morgoth [or >] and regain what he stole.'

Christopher Tolkien's 'a good deal of alteration in the narrative of The Silmarillion' refers to the revised story as a whole, but this late version is problematic with respect to more than one matter, and contradicts Galadriel's (and Celeborn's) history as published in The Road Goes Ever On.

It's possible (if pure speculation!) that the adumbrated tale never got beyond an adumbrated tale because Tolkien actually stopped to refresh his memory -- concerning what he had published about Galadriel, versus what he had merely written about her over the years -- though obviously other things are certainly 'possible' here. Tolkien would pass from this life soon enough after this late text was written, in any case.
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*Christopher Tolkien comments that this is strange, because all the progeny of Finwe were born in Aman.