Hmmm. Book smarts don't always equate perfectly to practical skills. Hermione is very clever, and undoubtedly better at casting spells (as we seen in classes where she is always the first to charm, transfigure etc. whatever she is working on)... but a duel is a different kettle of fish.
Harry has a kind of luck, quick thinking and reflexes, basically the instincts that have seen him survive a near duel with Voldermort once, be the single unharmed one from the Department of Mysteries battles etc. Which is what Hermione said to him with the DA club business - Harry is just is good at that kind of thing. And Hermione can get flustered - remember in the PS were she momentarily froze when Ron was being strangled by the Devils snare?
Still, if it was a duel on skill alone, I'd probably give it to Hermione - after all, she knows how to silently cast, probably has a wider variety of spells (her bird missiles from HBP anyone?), is probably more tactical... but if this was in terms of characterisation then I'd give it to Harry. This is what he does, he doesn't get through things by being the smartest, or fastest, or strongest - but by talent and luck. And he is slightly better at practical defense against the dark arts, which seems to be were the main dueling skills come from.
Harry Potter is a lucky bastard and would probably win by pure luck. Come on we all know he survived Voldermorts murder attempt because of his mother. And every time there is a fight Harry gets saved in the most unlikely way by some strange thing. As in "the chamber of secrets" Harry could barely manege to fight Voldemort even tough Voldemort didn't actually live. Harry was just about to die when suddenly Dumbledores pheonix arrives. Lucky bastard. there are more examples. Hermione should win but ye never know with Harry. 😠