Firstly, Help is a transitive verb so it needs a direct object
A. This should help John understand why we believe method A to be correct
B. This should help John understanding why we believe method A to be correct
About understand and understanding. I would prefer to use A's sentence. There are special verbs in English that are followed by a direct object and a bare infinitive verb such as make and help.
You make me cry
For example, it always sounds better than you make me crying or you make me to cry.
However, I've done some research on internet that you should use to-infinitive in formal writing or speaking for the verb help.
This should help John to understand why we believe method A to be correct.
But personally, I think to is like an interference here. I'd still prefer the A's sentence.