The chin-up and the pull-up both work the same basic muscle groups, the lats, biceps and gripping muscles. Chin-ups are performed with a supinated grip (palms facing) and pull-ups are done with a pronated grip (palms facing away). Chin-ups are easier to perform because the biceps (prime mover) are in a more advantageous pulling position. The chin-up also strongly recruits the lats and the pecs. There are many variations of the chin-up that can target various parts of the upper torso. Keeping the back strongly arched and touching the sternum to the bar is a great lat, pec bicep exercise. Rounding the back and bringing the knees slightly foreward as the chin clears the bar, is a great bicep, lat, abdominal movement. In all chinning movements, it is important to keep the hands about shoulder width. Using a wider grip can cause elbow and shoulder injuries. The average college age trainee, 5'9", 155 lbs. can do 9 chin-ups. That would be equivalent to doing one chin with 35 lbs.
The pull-up is more difficult than the chin-up because the biceps cannot be fully utilized. The average male is 30% weaker in the pull-up than the chin-up. The pull-up became popular in physical education programs after WWII. It was found that many soldiers lacked the ability to pull themselves over high walls and fences. The military took steps to address this issue with the inclusion of pull-ups during basic training. This trickled down into the public school PE programs. The pull-up utilizes the upper body pulling muscles similar to climbing over a wall, fence, side of a ship or through a open window. Because the hands are pronated, the elbows move down and back during the pull. This places a strong emphasis on the rear shoulder girdle and upper back. With the pull-up, there is much less pectoral involvement. Also, the brachio-radialus, a large upper arm muscle under the bicep, is strongly involved. The pull-up mimicks 'real world' activity. In performance, the hand placement should be slightly wider than shoulder width. At the top, attempt to touch the throat foreward to the bar. Be careful of certain close grip variations like sternum pull-ups. These can really irritate the elbows.
The weak link in both exercises is the grip and upper arm. These muscles always fatigue much sooner than the large muscles of the upper back and rear shoulder. I tend to think of these movements more as upper arm and grip exercises than back exercises. For body building purposes, stick with the chin-up. For tactical and functional strength, go with pull-ups.