Among historical fiction writers, the authenticity vs. accuracy debate is a thing. That is, depending on the kind of historical fiction you're writing, you are going to have to balance historical accuracy, the absolute facts: the year of certain Big Events, the layout of cities and towns in whatever era you are writing, the politics and social conventions of the time, the clothing, attitudes, maybe even language.
I guess I'd say authenticity is integrating all the factual things with the elements of fiction--characters, a plot, atmosphere, dialogue--and making the history work in the context of the story (and with your perspective of the history)--and to make sure all of that is readable and entertaining.
So, which is more important? I've read historical novels that were purported to be "extremely accurate"--but then, how can we sure about that? Beyond a certain point, we don't know what happened or how things were back then actuality because everyone from that time period is dead. Complete accuracy isn't always compatible with a story, either. Of course, if you're writing about a real historical person, then I expect a high level of accuracy and then really good educated guesses to fill in the gaps.
I read historicals because I enjoy them. If I'm reading historical romance, it's because I want to read a (slightly implausible) (okay, fine, often very implausible) dramatic love story set in the past, because the past had trends, events, and attitudes that I like learning about or seeing exhibited within a story. I learn history better when it comes alive in fiction; it's only the past couple of years that I've found history books with good narrative that drew me in just as well as historical fiction does.
I suppose that's authenticity--when the factual, pedantic stuff of history research melds into a certain feel or attitude or event that feels plausible and makes for a good story?
What would you say is historical authenticity?
In the historical romance world, there's a term for stories that are more costume drama--characters who dress up and live in the past, but where the history doesn't really impact on the characters: wallpaper historical. It's not a compliment. When I submitted the first version of the Keegans, which at the time was a Regency historical romance, to a contest, the feedback I got back included: "You're not writing a history book!"
I swear, it was like two paragraphs of description about the Bristol port, since my characters were seeing it for the first time.
So, for instance: Pearl takes place in the late 1790s. Complete accuracy would have had me describing the graphically brutal treatment slaves in Barbados received in that time period--and likely, if I was being totally accurate, Pearl would have never found Julius. She might not have been freed or Miles would have treated her like an object or the various wars England was fighting would have been more prominent or the complicated politics of England at the time would have more directly affected my characters. And while some of that would have made a compelling story, it's not the one I was trying to tell. Whether it feels authentic enough is up to the reader.
My short story with the long title "The Disappearance of Miss Mary Dawkins" is a bit more wallpaper-y. A young woman is pregnant with an illegitimate child and doesn't know what to do with her future, so she ignores it for as long as she can until she can't anymore. It happens today, it happened in many historical periods, and there isn't much that's integral to the story that made it have to be set in 1793, except that Mary Dawkins is the mother of a character in Pearl and that character was born in 1794.
My current WIP is shaping up to be a bit more on the accurate end of things than the other two, because there are a few real people in it as minor and background characters, so I need to be sure they're in London in the spring and summer of 1894, for one thing. The main characters aren't real historical figures, but they do take different paths in their lives and their stories, so I'm going for an authentic late Victorian feel in their mindsets and attitudes rather than researching American heiress wives of English lordlings to death or having a character immediately jump into an idea of having a career or attending university because in that time, those decisions would not have happened in a split second.
For me, remembering that I'm telling a story--a fictional story--is the key.
How To Write Historical Fiction: 7 Tips on Accuracy and Authenticity
Hilary Mantel and the Limits of Historical Accuracy
On Wallpaper Historicals