How is Analects split up in English? Chapters? Verses?
Comparing with the Bible, I think Book/Chapter would be the most accurate.  Each 篇 revolves around one specific aspect of Confucius' ideas, and each 章 is a (mostly self-contained) event/story.

Unlike the Bible, in which the chapters/stories usually follow a chronological order within one book, there is little interdependence between chapters in 论语.  But I would argue that, if one is to extract Jesus's words from each chapter of Bible, one would probably get something of size comparable to a 章.  Therefore it is quite reasonable to make 篇/章 correspond to Book/Chapter.