Reasons for punching too slowly include a bad technique and an unhelpful mindset. For punching effectively (and not so slowly), you need the right technique, posture, breathing, distance from opponent, and attitude.
The difference between boxing and karate is that boxing focuses on punching to take opponents down quickly. It is best for street fighting. Unlike boxing, karate is a complex system of forms and techniques with an underlying philosophy. It is ideal for professional fighting. Both disciplines, however, work well in MMA.
You can spar with training gloves. Both sparring gloves and training gloves protect your opponent but training gloves also give more protection to your hands. This means that sparring in training gloves provides less real-world training than sparring in sparring gloves, which are meant to mimic real fights as closely as possible.