Answer
In both cases, the impulse that the hand exerts on the ball is the same. However, when we catch a ball with a bare hand, the time of the collision is less than the time of the collision when we use a padded glove.
Since the time of the collision is less when we use a bare hand, the average force exerted by the bare hand must be greater than the average force exerted when we use a padded glove. Since the average force is less when we use a padded glove, it feels better to catch a hard ball when wearing a padded glove.
Work Step by Step
In both cases, the impulse that the hand exerts on the ball is the same. However, when we catch a ball with a bare hand, the time of the collision is less than the time of the collision when we use a padded glove.
Since the time of the collision is less when we use a bare hand, the average force exerted by the bare hand must be greater than the average force exerted when we use a padded glove. Since the average force is less when we use a padded glove, it feels better to catch a hard ball when wearing a padded glove.