Both get a a +2 to persuasion from a 14 charisma. Being a paladin doesn't change anything. A paladin may get more combat benefits from that 14 charisma, the OOC benefits are the same, which is what I thought this discussion was about.
Unless you're just changing the goalposts of course.
The Out of Combat is not the same. The Paladin has social and exploration spells. The Fighter has none.
Heck even a ranger with negative Charisma has better social strength because they can talk to animals and plants and get bonus languages which open up semi-exclusive silos withi the pillar.
And getting that Fighter's OOC strength up requires sacrifice of combat power via a fighting style or feat.
I mean it would have been enough to have a fighter choose between City Watch, Gladiator, Self Taught, Streets, Tribe, or Tutor and get +1d4 to a niche situation.