The veteran stuff has what will feel more like the director's cut sort of stuff, the goofier stuff, and the VO that was just too distracting or over the top for the first experience. The recruit will mainly funny things where they make fun of you for being a total noob.
I'd recommend doing a play through on a "standard" background, then recruit, than veteran, not because of the dialog choices, but because with three playthroughs, you will see a decent chunk of the branching content. Not nearly all of it, but with three playthroughs, you'll see just how big of a game you have with AP.