I'm not too familiar with the story collection known as "One Hundred and One Nights" which, according to The Arabian Nights Encyclopedia originated from North Africa and contains some elements of the familiar stories from some of the oldest versions of the 1001 Nights. If someone can point toward a copy for sale somewhere online or elsewhere I'd appreciate it (it's only in Arabic and French I believe).
From the encyclopedia: "The work is structured as a frame story resembling the frame story of the Arabian Nights, with the motifs of adultery, the cycle of marriage and execution, and the figures of Shahrazad and Dinarzad (Dunyazad). The collection contains eighteen stories. These stories are similar to well-known stories in the Arabian Nights such as Uns al-Wujud and al-Ward fi'l-Akman, Ni'ma and Nu'm, The Three Apples, and Hasan of Basra. The Mi'at Layla wa-layla also contains versions of the Book of Sindbad, The Ebony Horse, and The City of Brass" (vol 2 594-5).
The encyclopedia also says these stories were written in the 19th century, well after the main known Arabic versions of the 1001 Nights.
A recent news article featuring German scholar and translator Claudia Ott suggests that she has found a manuscript of the 101 Nights which predates even Galland's Syrian manuscript which is, if true, one of the most significant manuscript findings in the Nights' history. The article suggests that this 101 Nights' manuscript dates from the 13th century which, apart from the Nabia Abbott fragment, would be the oldest manuscript for any stories relating to the 1001 Nights.
Whether or not this manuscript is indeed as old as they are claiming and what stories it contains remains to be seen but it is a very very interesting development nonetheless.
Here is the link to the article/interview with Ott: http://www.qantara.de/webcom/show_article.php/_c-310/_nr-761/i.html
from the article:
"However, there are divergent opinions on the relationship between the two books. There is already a critical edition of the "101 Nights" based on much more recent manuscripts from the late 18th and early 19th centuries, whose publisher, Mahmud Tarshuna, claims that "101 Nights" is the substantially older and more original text. His argument uses motifs from the framing narrative to claim that the "101 Nights" is closer to the Sanskrit and Pali texts of their old Indian literary sources than "1001 Nights" is.
But we also have some very old sources for "1001 Nights". In Chicago in 1949, a double sheet of paper was discovered in a pile of papyrus that had been brought back from Egypt. It bore the title "Thousand Nights" ("alf layla" in Arabic) and the beginning of a description of one night. The double sheet is a palimpsest dated 879. Its origins are evidently not Egyptian, where papyrus was still preferred to paper at that time, but Syrian."
"This also fits with what the Arabic sources tell us. Contemporary booksellers reports make it clear that a complete version, with 1000 Nights, must already have existed in the 9th century. Over the centuries several fragments of the work have been found, each of which have probably looked rather different from one another. The 1001st night was probably added in the early 12th century. In a notebook, discovered by chance in the Geniza in a synagogue in Cairo, there is the first known mention of the complete title on a lending note from around 1150: "Alf layla wa-layla" – "The Thousand and One Nights".
So I am convinced that "101Nights" and "1001 Nights" are part of a parallel tradition. "The Hundred and One Nights" and "The Thousand and One Nights" were contemporaneous with one another, the one probably better known in the west, the other in the east of the Arabian world. But all of this is something that requires further investigation. A magnificent chapter in Arab literary history has just been reopened."