We're much stronger doing chin-ups (palms facing you, narrower grip) than we are doing pull-ups (palms facing away, wider grip) because we have a better mechanical advantage in the arm position.
With this is mind, you can combine the two exercises into one drop set by beginning with the most difficult variation and progressively "working down" to the easiest version. As you fatigue, the exercises become easier, allowing you to continue to crank out high-quality reps.