The question is nonsensical. What requires a faster reaction time? In relation to what action or result with a batter?
Relating to the tennis portion: Are we interested in reaction time to serve a tennis ball or to return a serve from another player?
In both cases, the mental time to react to the very beginning of a pitch or the very beginning of a tennis serve is the same. Meaning the time the brain recognizes a ball will be flying towards the receiver very soon in either situation is the same.