While I like Pegg’s work as a writer (Shaun of the Dead, Hot Fuzz, etc), I’m not sure how that will fit with the more serious Star Trek. Unless they’re going more for a “The Voyage Home” vibe with this film. I do know he’s a huge Sci-Fi fan and has been vocal about his love of the franchise.
Jung, on the other hand, has few writing credits, none of which seem to include any genre TV or film.
With about a year and half left until its release, the film has been plagued by problems with its script and directors.