Mr. Woodifield and the boss are around the same age. (There's only a five year age gap between them). It would be safe to conclude that they've gone through many of the same experiences, the most important of which would be losing their sons in the First World War. To some extent, the men are on the same wavelength. They know what it's like to lose a son and so can identify with each other in a way that would be impossible for someone who hasn't gone through a similarly traumatic experience.
Nevertheless, the differences between the two men are quite significant. Uppermost of these would be their respective ways of dealing with grief. The boss talks about his daughters' recent visit to his son's grave without displaying much emotion. This would appear to indicate, though we cannot be absolutely sure, that he's been able to deal with his grief more effectively than Woodifield, who remains emotionally destroyed by the tragic loss of his son.
That said, Woodifield is similar to the boss in that he's able to keep his true emotions in check in front of others. Perhaps the boss also displays the true depths of his grief in private. If that is the case, then that would be something else he has in common with Mr. Woodifield.