The answer is the more active you are the better you will do, why ? because the more ur body adapts and generates the right muscle fibres for the job.
Type I Fibres
These fibres, also called slow twitch or slow oxidative fibres, contain large amounts of myoglobin, many mitochondria and many blood capillaries . Type I fibres are red, split ATP at a slow rate, have a slow contraction velocity, very resistant to to, fatigue and have a high capacity to generate ATP by oxidative metabolic processes. Such fibres are found in large numbers in the postural muscles of the neck.
Type II A Fibres
These fibres, also called fast twitch or fast oxidative fibres, contain very large amounts of myoglobin, very many mitochondria and very many blood capillaries. Type II A fibres are red, have a very high capacity for generating ATP by oxidative metabolic processes, split ATP at a very rapid rate, have a fast contraction velocity and are resistant to fatigue. Such fibres are infrequently found in humans.
Type II B Fibres
These fibres, also called fast twitch or fast glycolytic fibres, contain a low content of myoglobin, relatively few mitochondria, relatively few blood capillaries and large amounts glycogen. Type II B fibres are white, geared to generate ATP by anaerobic metabolic processes, not able to supply skeletal muscle fibres continuously with sufficient ATP, fatigue easily, split ATP at a fast rate and have a fast contraction velocity. Such fibres are found in large numbers in the muscles of the arms.
Fibre type modification
Various types of exercises can bring about changes in the fibres in a skeletal muscle. Endurance type exercises, such as running or swimming, cause a gradual transformation of type II B fibres into type II A fibres. The transformed muscle fibres show a slight increase in diameter, mitochondria, blood capillaries, and strength. Endurance exercises result in cardiovascular and respiratory changes that cause skeletal muscles to receive better supplies of oxygen and carbohydrates but do not contribute to muscle mass. On the other hand, exercises that require great strength for short periods of time, such as weight lifting, produce an increase in the size and strength of type II B fibres. The increase in size is due to increased synthesis of thin and thick myofilaments. The overall result is that the person develops large muscles.
Therefore the fibres that will form over time when doing alot of chin ups type II B fibres may be dominant. Or whatever type works best for chin ups.