I'm new to the site, but recently did a paper on this very subject.
In both the ???chin-up??? and ???pull-up???, the prime mover is the Latissimus Dorsi. They are both synergized by the brachialis, brachioradialis, biceps brachii, Teres Major, Teres Minor, Deltoid, and infrapinatus muscles. They are stabilized by the Pectoralis, Trapezius, Triceps, and Rectus Abdominis muscles. Aditionally, your grip requires considerable forearm strength.
The difference between the two lies in the poisoning of the grip. The start of both movements involves drawing your shoulder blades together (scapular retraction). This portion of the movement involves your back muscles and begins the lift. It also keeps tension on the back throughout the movement. During a pull-up, the angle of your wrist, elbow, and shoulders will change. The next portion of the movement involves drawing your body upwards. This requires flexion of the elbow joint, In order to flex the elbow joint, the biceps and supporting muscles are called into play. This, is the next critical link in the pull-up: your biceps. The brachialis is the strongest flexor of the elbow. Unlike the biceps, the brachialis does not insert on the radius, and therefore cannot participate in pronation/supination of the forearm. The brachioradialis is a stronger elbow flexor when the forearm is in a midposition between supination and pronation at the radioulnar joint. Paralel grip (semi-supinated) give the elbow flexors and shoulder extensors their most effective pull and is the form where you are most likely to use additional weight. When pronated, the brachioradialis is more active during elbow flexion since the bicepts brachii is in a mechanical disadvantage.
I can do several more ???chin-ups??? than I can ???pull-ups???, since my arms are assisting me more during the ???chin-up???. It seems to me that a ???pull-up??? would be a more effective exercise for the Latissimus Dorsi. However, there is no ???right??? or ???wrong??? grip for performing the pull-up, but rather, we should train using a variety of grips to recruit as many muscles as possible. Using a narrow supinated grip (4 to 6 inches between hands) will increase the load on the elbow flexors and also the torso. A narrow pronated grip as in a pull-up, increases the amount of load on the brachialis and brachio-radials muscles because in this position, the biceps brachii have a poor line of pull. This could be a good additional exercise for developing your brachilis muscles.
hope this helps,
Cheers!