I don't think there's a single best method to teach Latin. It's always a toss-up between different methods, each one has advantages and disadvantages. Personally, I would have trouble with Cambridge because it forces you to waste effort and time trying to deduce grammar from examples, which drives some students nuts, but others who are turned off by formal grammar will appreciate this softer approach of Cambridge. In LLPSI, the goal of getting you to think in Latin is a noble idea, but at the same time it takes away one of the student's most useful tools (his native language). I agree that the native language should be done away with eventually, but only when enough Latin has been acquired to be able to explain things in Latin.
The main problem in any method is trying to have the student read unadapted Latin too quickly. There's no way any student is going to read anything original (except perhaps the Vulgate) after only a beginner's textbook. This error has plagued Latin pedagogy since the 19th century when students were expected to read straight-up Caesar immediately after having completed the beginner's textbook. It produces students who do nothing more than decode, taking an hour per page, and who are only good at wearing out dictionaries.
Students will of course eventually hit the famous "barrier," usually when they start reading non-annotated editions of the authors. There is no method, and no amount of intermediate reading, that will completely prepare them for the "barrier," and there is nothing they can do except buckle up and plow through something on the order of 100 000 words, underlining problematic passages and using whatever means are available to understand them (dictionary, teacher, commentary, translation). The "barrier" exists in learning modern languages: there's a moment when something inside the learner clicks into place and he seems to suddenly understand people around him whereas before he only heard gibberish. In Latin, the immersion takes place by lots and lots of reading.
Personally, my method of choice is the old fashioned grammar-translation method followed up immediately (or concurrently) with lots of intermediate reading (Ritchie's Fabulae Faciles, Lhomond's Epitome Historiae Sacrae and De Viris), then books 1-10 of Livy, an hour a day.