How to make an iPad backup when buying a new device?
There are really only two ways to back up your iPad. Both of them are comphrehensive and should transfer everything onto a new iPad. Chances are, the space difference is comprised of music, and movies, and such that you can re-download from iTunes. iCloud will handle that part automatically, and iTunes probably won't. But, it's not hard to do.
Option 1: iCloud
iCloud is likely the easiest backup solution. Configure it in Settings &gt; iCloud, and make sure the initial backup completes before wiping your device. This is a helpful article including information that is backed up. The only thing is there is a 5GB free storage limit. After that, you will need to purchase more storage (for a nominal fee).
Option 2: iTunes
The traditional way of backing up iOS data, this way still stands strong and true. iTunes should backup all your needed data. Check out this great article about iTunes backups. I didn't find a specific mention of iBooks PDFs (which should be stored in iTunes, correct?), but it did mention on the 3rd bullet:

Application settings, preferences, and data, including documents.

This likely includes iBooks PDFs.
So, in summary, iCloud is likely going to be your best, easiest, and most user friendly way to backup. If it were me, I would do both. I have restored a backup from iCloud and found it remarkably easy and simple.