There are other journals out there (the diary of Miriam Watternberg, for instance, details life in the Warsaw ghetto, though this list contains many others), certainly. One reason Anne Frank's diary is so popular is because it gained a great deal of popularity early on, eclipsing later works and even suppressing them. The fact that here was a play and a film of it too helped cement its popularity.

However, I'd argue the more important aspect is in the work itself. Anne Frank's diary talks not only about the abstract evil of the Holocaust and the more pressing difficulties of everyday life, but also about Anne's own process of growing up. Her writings about her crush on the boy hiding with them and about her changing body are very, very relatable to a preteen and teenage audience, and help humanise the Holocaust in a way that Eli Wiesel or Primo Levi can't. It allows the reader to understand Anne Frank more as a human being, and so makes the tragedy of it all greater.

Basically, "The Diary of Anne Frank" has a combination of good time and very good readability.