Improved Muscle Development
As mentioned, the control of the movement is what encourages better muscle development and endurance. Moving too quickly against the resistance offers minimal increases to your muscles and strength.
Resistance bands counter this by providing better resistance both ways when controlled. The execution of the movement is only one point. Controlling the resistance, which is called the eccentric phase, is where all the muscle growth occurs the most.
An example would be performing a resistance band row by attachment to a stable object like a small tree. Execution of the row is pulling the bands towards you, but the control portion is not letting the band sling forward.
Dumbbells can still be controlled in the same manner, although the supporting muscles to control are not used as much. Being active either way is important, but if you can be more effective, then resistance bands are a great choice.
Increased Flexibility and Mobility
There is a large variety of exercises you can perform with resistance bands only. The use of free weight for lots of the exercises is almost meaningless or impossible. The reason for this the way the movement is performed, requiring elasticity over solid weight.
Mobility is having a healthy range of motions with your joints. Flexibility is the elasticity of your skeletal muscles to move across ranges of motion. Both are important for better health and to prevent injuries from occurring from simple tasks such as twisting your body carrying a box.
Not being able to perform basic life tasks is also due to a lack of muscle and bone strength to support joint mobility. Resistance bands offer ease of movement for those recovering from an injury or in their senior years. This is why they are an effective tool used by physical therapists.