I'm not quite sure of what you're asking, but both of your sentences are grammatically correct. You're making a comparison/contrast between two books, and making an observation about both. Either is valid, depending on what you're looking at

I agree with Dan. If I heard or read “This book is three times thicker than that one” I would think, “if that book is one inch thick, then this book is three inches thick.” I would think the same if I heard/read “This book is three times as thick as that one”. “Times” implies that a multiplication is involved, not an addition. If the sentence were “this book is 300% thicker than that one”, then I would think, “if that book is one inch thick, then this book is 4 inches thick.” (However, even in this case, I think that many people who are not mathematically inclined would not immediately realize the difference.)

Yes, there is an ambiguity in statements of this kind, and, really, it is the responsibility of the speaker or writer to phrase it differently so that there is no possible misunderstanding. It might be clearer in a real-life context, e.g. with money. As a native speaker, knowing nothing more, I wouldn't interpret it as a precise statement anyway. Nevertheless, my first guess is that meaning (a) is intended, because if meaning (b) were intended, I would have expected a different wording--such as "this book is 300% thicker than that one." The appearance of the word "times" is a powerful indicator for meaning (a). I would interpret the sentence as a sloppy shortening or abbreviation of "this book is thicker than--three time as thick as--that book."

I understand your confusion. I think that many (or most) people will think that “three times thicker”=”three times as thick” But in my opinion “three times thicker” is ambiguous and I would avoid using it myself. Logically it ought to mean “four times as thick” in my opinion.