I used the Sharper Edge book for my AIRAT and felt it was inadequate, but should more than suffice for the Class 4/AIRAF. I haven't personally used the Pultz Manual, but a senior instructor/former colleague had some kind words for it. More than anything else, I would highly recommend you read and re-read the FIG, FTM and the Human Factors book(s) that TC publishes. The sharper edge is probably a good review tool with their quizzes. But there's the he-who-must-not-be-named author (C***h@ne) who sells AIRAT quiz books for $129 which might be worth a look if you are interested...
I used Pultz when I was going for my initial. It's chalked full of good information. When it came time to upgrade, I tried using Sharper Edge, but a friend had told me to stick with the FIG and Pultz, I did that and everything went smooth. I definitely recommend Pultz.