TRY BOTH STYLES OF TRAINING!
The "tempo" or "speed" of a repetition, like your rest time, depends on the goal of the cycle of training you are currently on. A training program designed to focus on stability or "joint integrity" will typically use a slower eccentric or negative portion of a rep while keeping the concentric fast. Your program may also use slower eccentric times to create a desired fatigue of the muscle to improve muscular endurance, stability, or beginning strength. This is mostly used in the beginning of a macrocycle, which is kind of a reset once you have peaked at your goal.
Faster tempo reps typically are used for strength improvement, power development, and once again, muscle fatigue. Faster reps are typically used to improve performance in larger, compound, or heavy lifts for strength training and lighter weights, 30-50% 1RM for power training.
Both methods of training deplete glycogen stores in the muscle, develop lactic acid showing similar effects on muscle fatigue. It is thought that slower repetitions increase the time under tension, resulting in improved muscle hypertrophy. Research has shown this is not true. Total time under tension is equivalent between the two with the appropriate amount of volume. -
In the right training program, however, slower "TUT" being inferior to the possible effect of hypertrophy. This is due to the ability to use higher weight in high-speed reps, and the ability of the body to pump more blood to the muscle. This engages and breaks down more muscle fibers and delivers an increased amount foR resources such as oxygen to the muscles.