You can certainly take the whole CAO in if you like, however I only took the parts that I knew were relevant (I think it was CAO 20.7.0, 20.7.1, 20.7.1B, 20.7.2, 20.7.4 and some of the 82.0 series). Having each of those sections ready to go made it much easier than flicking through a big book full of info to find what I needed.
The advantage of Jepps is simple. They are what you will end up using later in your career anyway (assuming airlines of some description are in your future, which since you're sitting ATPL is a fair assumption I reckon) so get used to using them early.