I usually also got better grade, maybe because I had clearer idea about what lecturer focused on.
Video lectures on coursera were much more effective for me then live lectures. The difference was in speed up, slow down, rewind and stop buttons of course.
Exactly. The book covers a much wider range of topics. The lecture just clues you in on what the teacher is going to include on the exam.
Compare something like Schaum's Outlines to an undergraduate text for the same material for an example of what I mean. The outlines are pretty pruned down.
edit: just to add one more thought: we read all the time about "opinionated software." Pruning down the material requires understanding and "opinion" in the same way --- textbook authors almost invariably have the understanding, but are usually economically discouraged from imposing their opinion on the material because it can discourage book sales because instructors with different opinions tend to choose a different book. Lecturers don't have the same concerns, so they can prune more aggressively. Authors of textbooks that will never sell well (e.g. the advanced texts I mentioned earlier) don't have the same concerns either since they're never going to make a substantial amount of money off the book, so they can prune pretty heavily too.
Plus, while it may make sense for textbook to contain five different explanations, theories or proofs or whatever on X, it makes even more sense for professor to require only the most important of them.