I'm going to pull up this old thread instead of using my other one since there's already a discussion on it. Having read both Ajahn Brahm's book and (recently) Catherine Shaila's...I have a couple of thoughts.
Ajahn Brahm's teaching is very traditional and close to the methods mention in the sutta. Catherine Shaila's, on the other hand, is more "modernized" and apparently easier to understand/relate to. I like the way Catherine Shaila dedicates each jhana level to strengthening insight meditation. There is a more balanced approach to the uses of jhana. Ajahn Brahm sticks strictly to pure samathat until a certain proficiency is attained before using jhana as a tool to springboard into vipassana. Both methods work fine, depending on your temperament.
However, I do feel that Catherine Shaila has somehow "over simplified"/misclassified jhana levels and I have some concerns over how close it is to the Buddha's teaching of jhana. For instance, Catherine Shaila mentions in her book (for one of the exercises) that practitioners should attempt going from access concentration direct to first jhana, access concentration direct to second jhana, access concentration direct to third jhana, access concentration direct to fourth jhana. This does not fall in line with the Buddha's teaching that jhana has to be "moved up" chronologically.
Nonetheless, both are interesting reads.
~ swimming upstream is tough work! ~