Ibooks

If you have automatic downloads for ibooks turned 'on' on the iPhone then any ibook purchases that you make should also download onto your phone. If you are saving epubs or PDFs into iBooks on your iPad then you will need to sync them to the iPhone as well - iBooks can keep collections in sync between your devices via Settings > iBooks but the content needs to be on there first e.g. if you move a PDF into a collection on the iPad, then if the PDF is also in iBooks on your iPhone then it should be automatically moved into that collection on the phone, but it won't copy the item to the phone if it isn't on it.