The other book is Unlocking Android from Ableson, Collins and Sen (Manning, ~29$).
This book definitely has higher ambitions. It is longer than the previous one (~400 vs. ~200 pages) and expects sequential reading. Beside the usual topics, it ventures into such exotic areas like Linux-level programming in C in the Android environment. Curiously, this breadth of topics means that the Manning book deals less with UI-programming than Burnette's book (82 pages in the Burnette book vs. 62 pages in the Manning book).The Manning book does provide, however, a detailed view of Android programming model. It discusses Android services extensively and even presents, how to write a content provider (although not in detail).
To summarize, the two books follow different concepts. Burnette's book is, erm, pragmatic. It tries to make the reader productive as quickly as possible using the most common application type, the UI-intensive standalone application, with some web programming thrown in for good measure. Meanwhile, it omits a great deal of Android architecture. The Manning book builds systematically, by presenting the architectural concepts in detail. Decide yourself, which one suits you most. I enjoyed reading both.