These were quite popular after the Krashen years, and never really went away, partly because they were successful and popular, and partly because it is difficult to change a program entirely, so people don't want to do it unless there are really good reasons for it. It has probably not been proven statistically or conclusively that they are better than skills-based programs; in fact, in content-based programs, teachers tend toward skills-based activities, while in skills-based programs, teachers tend toward content-based activities.
The theory of content-based programs is simple. While investigating a single topic thoroughly, students get immersed in that topic, as they would in an academic setting. They learn vocabulary and grammar in the service of pursuing real, authentic information and soon get immersed in the topic itself, forgetting how painful it is just to study vocabulary and grammar (for example) for its own sake. In pursuing an academic subject as they would if in an academic class, they get immersed in the vocabulary of that subject, get enough repetition of that vocabulary to have some success in dealing with related topics, build a better general vocabulary from there.
For example, our highest level leads students through an environmental textbook, giving both readings and listenings in the same "Core" course, ten hours a week. The writing class, another eight, leads students to use the material to write an environmental research paper so that they can use what they have read, yet hopefully write something that is not plagiarized but uses the concepts of the core class. Our second-highest level is similar but uses more behavioral psychology topics.
The obvious problem with devoting 18 hours a week to a single topic is that students might get tired of it; they also might feel that certain topics unfairly benefit those who happen to have a background in that topic (this happens when we switch to business. We've also used astronomy, economics, anthropology, and sociology). One justification is that in the university (where we are), students will be required to take one science class anyway, or perhaps one humanities class, as an overview or introduction; what we ask of them is presumably not so different, and actually broadens their horizons. On the other hand, a valid criticism is that after 8 weeks, they know a lot about environmentalism, but nothing about twenty or so other topics that may appear on the TOEFL; we are but scratching the surface of the sum total of everything they will need.
The one obvious advantage is that a movie can now supplement the textbook in a major way: by providing a background and by allowing students to hear all the words they are reading, sometimes repeatedly. This cannot be done or isn't done in skills-based programs.
My own philosophy on the nature of the curriculum is stated above; it is that it is not as important, by itself, as it seems. In our program teachers tend toward saying, "Now we'll do listening", while, in a skills-based course, a Reading teacher tends to say, "The next few readings will be about X" thus setting up a kind of context-based class anyway. Thus students seem to do well in both programs, and it's barely worth changing. Most of the programs that changed over to content-based programs have stayed that way. Textbooks have straddled the line, trying to serve everyone. Most people assume and live with a large amount of crossover material in skills books.