Short form: Is the Dueling enhancement from the Pathfinder Society Field Guide legal and available for PFS play?
The Pathfinder Society Field Guide is listed as a legal resource, and nothing that I've seen specifically excludes the Dueling enhancement from that legality.
The Ultimate Equipment includes a completely different take on an enhancement called Dueling. Different benefits and different cost.
Traditionally, large shared campaigns have mandated that when you have a name duplicated like that, you must use the newest legal published version of the ability. I previously had a Venture Captain remind me of that when he said that he thought that meant I could no longer take the PSFG version of the enhancement.
Looking through the Year of the Demon Organized Play Guide on Page 27, under Playtests and Errata, I found the following statement:
If a feat or trait changes or is removed from the Additional Resources list: You have two options. First, you may either switch the old feat for an updated feat of the same name in another legal source (if available), ignoring any prerequisites of the new feat you do not meet. Alternatively, you may replace the feat entirely with another feat for which you meet all the prerequisites.
While that doesn't seem directly applicable, it does seem to indicate that PFS considers that multiple things of the same type with the same name can be legal at the same time.
Thus, I return to an old question: Is the Dueling enhancement from the Pathfinder Society Field Guide legal and available for PFS play?