This essay is kind of simplistic but still offers a decent overview of some of the more controversial points regarding Burton's use of Payne in Burton's translation.
It doesn't really have a title but it's called "criticism" on the 1001 Nights' "Answers.com" page.
The essay: http://www.answers.com/topic/the-arabian-nights-story-7
I don't agree with the author's assessment of Burton not "deserving" the attention that his version of the Nights received for many important reasons and I don't agree that Burton's version outshone Payne's because of "sex" - I think much more importantly Burton's version was more popular and has been more popular than Payne's because of Burton himself.
Like all modern authors shaping their own identities Burton's life history and controversy shaped the reception of his translation much more than his inclusion of sex, though Burton's notes are, to be sure, the most often talked about things when people talk about his translation.
Too much of this essay relies on Mia Gerhardt's book on the Nights as well. Gerhardt's book is important to be sure but basing your essay's thesis on her assertions and claims of plagiarism (which were pre-research suggesting otherwise - see Mary Lovell's biography of Burton for example) is not conclusive enough I think.
From the essay:
"Burton, however, was never deserving of that reputation. His version was essentially plagiarized, with some modifications, from an existing translation by John Payne. While some of his revisions improved Payne's work, many of them gave the text an archaic and formal feel that bears little relationship to the original. The real "value" that Burton gave to the work was to be found in his salesmanship, and for that he relied on his potential readership's age-old desire, despite the veneer of Victorian prudishness, for sex. Burton knew, long before the advent of Madison Avenue marketing campaigns, that sex, particularly exotic sex, sells, and he made certain that his version of The Arabian Nights had plenty of it."