What is more I detailed the difficulty that arises in such an investigation where it is one person's word against another.
What is more I detailed the difficulty that arises in such an investigation, certain aspects of which are a case of one person's word against another.
The primary difference between these two sentences is that (2) is very explicitly noting that "one person's word against another" is only part of the important details of the investigation. (1) does not do this and it could be inferred that the detailed difficulty is only related to investigations that entirely revolve around "one person's word against another".
It doesn't inherently imply this but that would be the only significant reason to choose (2) over (1).
As an aside, both sentences could use some further proofing. An example:
Furthermore, [the report] details the difficulty that arises in investigations where certain aspects of the case involve one person's word against another's.