I've got an AIP lying about somewhere (2-3 years out of date). Is its comms section any better than Jepps?
No different. The AIP is the Australian legislation, so Jepps is required to reproduce it pretty well word-for-word, including the Comms, though in different paragraphs etc.
The IFG has some of the simpler calls explained, but nothing in detail.
I have found the IFG to be excellent, though strangely enough a lot of the calls in it are not really absolutely "standard" either, and not always as up-to-date as it might be, so some purists still eschew it. However, if you stick to those calls you will have no problems at all, IMHO.