Robert Mack's edition of Arabian Nights' Entertainments allows the reader to see the Nights how they looked to the first English readers as it is a (slightly) edited version of the first "Grub St" English edition which started appearing in England between 1706-1721.
(for a brief history of the Nights see the link - "What is the Arabian Nights" on this blog)
What strikes me as interesting so far is the frame story and how much emphasis it places on the reasons for Scheherazade wanting to marry "Schahriar" (as he is spelled here).
She seems particularly concerned with the future fates of her fellow townswomen, maybe more so than I recall any other version.
The background of Schahriar's unique marriage situation is explained as such:
"The rumor of this unparalleled barbarity occasioned a general consternation in the city, where there was nothing but crying and lamentation. Here a father in tears, and inconsolable for the loss of his daughter; and there tender mothers dreading lest theirs should have the same fate, making the air to resound beforehand with their groans. So that instead of the commendations and blessings which the sultan had hitherto received from his subjects, their mouths were now filled with imprecations against him" (10).
And Scheherazade comes to the rescue:
"I have a design to stop the course of that barbarity which the sultan exercises upon the families of this city. I would dispel those unjust fears which so many mothers have of losing their daughters in such a fatal manner" (10).
She later says "If I perish, my death will be glorious, and if I succeed, I shall do my country an important piece of service" (11).
Burton's edition has these reasons but they are backgrounded behind the necessity of Scheherazade as being next in line due to the lack of any other living marriageable young women:
"and mothers wept and parents fled with their daughters till there remained not in the city a young person fit for carnal copulation" (14)
and Scheherazade wants to "save both sides from destruction" (15), not just the townfolk, putting more of an emphasis on the innocence of Shahryar, that he was acting in some ways rationally given the betrayal of his wife (vs. the Grub Street edition which doesn't give him that much play)...
Another thing that is interesting to me is the set up of the storytelling, in Grub St. Dinarzade wakes her sister up before dawn in order to hear the rest of the story, when dawn comes Scheherazade stops (and promises to resume for her sister the next evening if she lives). Schahriar takes a backseat to the whole thing, kind of creepily listening in the dark and secretly being interested in the stories (vs. being the or a main person who listens and can't wait for the rest of the stories, as is more popularly portrayed).
Burton's has Scheherazade telling stories for the enjoyment of both her sister and her king: "'Tell on,' quoth the King who chanced to be sleepless and restless and therefore was pleased with the prospect of hearing her story" (24).