Both have their value. The annotated bibliography and the literature review, although they are very similar in many ways, are very separate in the general purpose they serve and the structure they follow. The annotated bibliography is just an organized listing of sources with brief overviews/summaries. This type of document is for readers who are looking for additional reading on a particular topic.
The literature review, on the other hand, is a document that explains and summarizes a particular topic while also compiling many sources/literatures to back up what is being discussed. Unlike the annotated bibliography, the literature review organizes everything into a cohesive whole in order to give the reader all they need to know on the topic at hand.
My own experience with the two is minimal, yet I have experimented with both throughout my time in school. In my undergrad, I was an English major, and the annotated bibliography was a popular assignment for a few classes I had taken. My experience with the literature review is less attempted and rehearsed. The literature review has only been come across in courses for my masters.
I understand the importance of both, but I prefer the literature review because of its interweaving of source material and author knowledge. The literature review, like the annotated bibliography, gives the reader a variety of sources that they may explore further if they choose to, but unlike the annotated bibliography, the literature review provides the reader with a much more streamlined and quick-to-understand summarization of what is known. In other words, the literature review is less work for the reader than the annotated bibliography is – this is only my opinion.
In terms of the writer and the process of writing, I still tend to favor the literature review. It calls for more work than the annotated bibliography, and it is simply more fun to write… less structured, methodical, and organized in a way. It is also more enjoyable to read. There is an introduction and conclusion to the piece that makes it more of a text and not a catalogue one must search through.