Upper back thickness, definitely dead lifts.
Pull ups/chin ups, the primary difference in palms facing toward or away from you is grip strength. Palms facing you relies on heavy recruitment of the biceps and your flexors in their strongest position and palms away relies primarily on your forearms. As far as which back muscles they hit, not different enough to be able to build a different looking physique whether palms facing toward or away. Bottom line, the lats are performing a vertical resistance. The plan of motion for the muscle is up & down, how your hands are turned effects primarily grip strength (how easy or hard it is to hang on). More often then not, the average person can do more pull ups with palms facing them, it's because you're involving more biceps, not because your incorporating a different part of your back as oppose to palms away (which again, is a heavier reliance on forearms then bi's, which is why most people can't do as many pull ups with palms facing away). I said "most" so if your an exception, then you have great forearm flexor(s) strength, more power to you.
Side note: Your strongest grip position on the pull up is palms facing each other (like doing pull ups on parallel bars). This recruits the brachioradialus, which is generally much stronger then your flexors or extensors, and this is also why hammer curls are generally stronger then supinated bicep curls.