A method book is a curriculum for piano learning where the material is put in a specific order to facilitate learning. These are textbooks for piano learning--and there are many different options nowadays.
So how do piano teachers decide which method book to use for beginners? Is it the price of the books? The illustrations and pictures? The number of books included in the method? The repertoire included? The teacher's familiarity with it because it's the method he used to learn piano as a kid? Or a combination of all of the above?
While these could all play a part in selecting a method book, the knowledgeable piano teacher familiar with Bruner's The Process of Education looks for and knows that the most important aspect is how concepts are taught and sequenced. And why are concepts and its structure important? Because the learning of properly sequenced concepts makes the subject easier to understand, easier to remember, easier to transfer, and it narrows the gap between the basic 5-finger pattern and Beethoven's Waldstein Sonata. We won't go into the details here, but needless to say, this was about the time I realized my piano performance degree from a music conservatory coupled with my natural interaction with children did NOT automatically qualify me to be a good piano teacher. There is so much more to educating your child than the ability to play piano and amicability.
Now armed with this knowledge, which piano method book is the best? Honestly? None. There isn't a "best" piano method because students don't all fit into one "best" student mold. Different kids have different personalities, abilities, learning style, and at different developmental stages cognitively. Sorry to disappoint if you came here looking for a definitive "best" piano method book. The truth is it takes serious work and study into a method because the best method book is the one the teacher knows the best. And I'm not talking about a used-it-when-I-was-little way, not even a have-taught-it-for-the-last-decade way, but know it best in terms of knowing the method's strengths and weaknesses for different types of students and learners. Know how to best supplement the weaknesses with other materials and how to make adjustments for different students.
I use the Celebrate Piano! Method books. I'm most familiar with this method book because of my pedagogy studies with Dr. Mitzi Kolar, one of the authors of the method book, and gained insight into the learning concepts and strategies in this method and the reason behind how concepts are taught and sequenced. And while no method book is perfect, this one comes close.
"If you are a creative teacher, you can teach any type of student with any method."