Both of these Snow White versions, two among many, are very lengthy, so a discussion of all the difference is not possible in this answer format. We can identify a couple of the first, and most striking, differences between them, though. Two of the first differences correspond to the origin of Snow White and the relationship between the central female characters; these pertain to characterization and the literary element of tone.
In Grimm's version, the Queen is characterized as a loving, though exceedingly vain woman. Her vanity has caused her no harm at the beginning of the story because there are no rivals in all the land to her beauty. Consequently, she can be loving and kind. It is as a kind queen that she wishes for a daughter whose beauty matches the whitest snow, the reddest blood, and the blackest ebony.
In contrast, in Sexton's version, Snow White is the daughter of a widowed King. His second Queen is the beautiful and exceedingly vain woman who is thrust upon Snow White's world; this is the stepmother also seen in Disney's Snow White. This Queen thinks little or nothing of Snow White:
had been no more important
than a dust mouse under the bed. (Sexton)
The second early difference of import is that while we can infer that Grimm's Queen mother is loving and kind to Snow White because (1) she requested Snow White and (2) there is no suggestion to the contrary,
"If only I had a child as white as snow, as red as blood, and as black as this frame." Soon afterward she had a little daughter that was as white as snow, as red as blood, and as black as ebony wood, and therefore they called her Little Snow-White. (Grimm)
it is made clear in Sexton's characterization that her version of the Queen puts a very different valuation on Snow White.
Snow White is described by Sexton's poetic persona--who has a bitter and unavailing tone--by comparing her to "cigarette paper" and "Limoges" porcelain and red wine from the Rhone Valley and a china doll with eyes that roll "open and shut" and a bonefish. When this is added to the Queen's perception of her as being no better than "a dust mouse under the bed," we recognize Sexton's is not an appealing kind of description, or characterization, though it leads to the same white and red coloring the Grimms give their Snow White. As you examine the remainder of the stories, look for continued differences in tone and mood as well as in the behavior of Snow White and the Queen.