In almost all the movies about the O.K. Corral fight (there have been almost 40 with more on the way) the producers seem to want to turn Doc Holliday and the Earps into cowboys. Kurt Russell as Wyatt, in 1993's "Tombstone," is wearing boots, instead of shoes, for example. And virtually all the re-enactors I've seen, who portray the Earps wear boots, often with their pants tucked into the tops, which probably would have been laughable to Nicholas's boys. And by all accounts, the Earps wore city style hats, with narrow brims, but all the actors who portray them want to increase the hat brim size to make it more "cowboy."
That said, Holliday did have on a broad-brimmed hat and according to one account was wearing a holster (all the Earps are described as putting their pistols in their pants, or coat pocket like gamblers on the sly).
Like "mission creep" the movies can't resist bending the styles to suite the fantasy of what these boys looked like. It's safe to say, the Earp boys preferred narrow brims, shiny shoes and natty ties and did not emulate cowboy clothes, at least in town. On the trail, or out on posses, I imagine they did resort to boots and broad brimmed hats, but in town, well, not so much. Still, the movies are trying to create a fantasy world where the Western can thrive and I certainly do want to cut them some slack on this.