The answer to the above question is “Both.” The sport ingredient, with the exception of the serve, is a race to the ball and the game ingredient is having a purpose for your shots.
Arriving in balance to meet the ball in front of the body is mainly the job of the legs, “lower body,” but combined closely with mental and even spiritual processes and actions some of which are paying attention, reacting, tracking the ball, and believing. Playing the ball with some plan is the result of understanding strategies of the game and mental awareness during the play bonded with Hands’ skills, “upper body.” Hands serve the purpose of holding and applying the tennis racquet, as an instrument. Hands amplify what the tool of the tennis racquet can do to the ball after legs deliver and initiate the racquet action. Think of musicians: their hands bring out the best out of the instruments, but the best artists use souls and hearts first. Same with tennis players. It is a huge advantage to have great hands, but they can only put the purpose into the shot, if it comes from the head, and only (!!), if they were brought to the ball on time by the “lower body” with unstoppable will and drive from the heart. I am clearly advocating and prioritizing the importance of legs and head in tennis, as much as the importance of hands with great feel and loose arms that gel and swing.