As everything else when it comes to fitness and training, you should always ask yourself. What is the focus and/or the purpose of doing an exercise?
With all those things in consideration, here’s a short breakdown on the two exercises:
The pull up develops the lat muscles (Latisimus Dorsi) because you have scapula downward and upward rotation. The lats are extremely important when it comes to speed development. 40% of your speed comes from your arms and the lats are responsible for “slamming” your arms downward with every stride you take or jump you make. “Slamming” your arms downward creates a “ground force reaction” which enhances every stride and jump. For example, if you just drop a basketball on the floor, it won’t bounce very high. If you “slam” the basketball on the floor it will bounce very high. Same thing with you generating a ground force reaction using your arms. The bicep muscle is the secondary muscle in this exercise.
The chin up is a more bicep dominated exercise which will develop your biceps. It is a safer exercise than the pull up since your arms are tucked in closer to your body. Now if you’re a bodybuilder or just want to look impressive on the beach, the chin up would be a good exercise to change up your “bicep day’ training regimen. As far as sports performance goes, I always tell my athletes, “I have never seen a bicep score a goal, point or run”.
Again, always ask yourself, what is the focus and/or purpose of doing an exercise?