The print version doesn't really add anything to the screen version other than fleshing scenes out more so they flow better. ADF has Mudd use his own means (hidden in his clothing) to manipulate Chapel's identity card rather than using a ship's computer terminal. What ADF doesn't do is manage to make Chapel and Spock behave much better than they do onscreen. That said, like in the other adaptations, the characters speak and behave with more nuance and it's easier to accept them as their live-action portrayals.
Overall the print version is moderately better than the televised episode, but not much given there being so little to work from.