This is a common question as both exercises involve extension of the fingers, so common sense would dictate that people should be able to just use a rubber band to defeat the effects of carpal tunnel syndrome by strengthening their extensor group.
The main problem with using a rubber band is that the finger extensors and finger abductors are the only muscles being exercised, and do not involve the wrist extensors which are a much larger group of muscles with most having two actions, the extension of the wrist and fingers. (Some are wrist extension only)
When using a rubber band to perform the extension exercises, there is a lack of range of motion that is performed, caused by several factors:
The first factor, that was left out of the video, is that you cannot bring your fingers down into a semi-closed fist position or the rubber band falls of the fingers. Therefore all of the finger joints cannot flex which completely narrows the scope of the effectiveness of the exercises. The more joints involved through their proper range of motion means better strength enhancing effects.
The second factor, which is mentioned in the video, is that you need to open and splay the fingers as far open as possible in order to stretch the flexor muscles, thenar and hypothenar emminence and the carpal ligament. The only way to keep the rubber bands on the fingers is to initiate movement at the base MP joint only and keep the fingers really stiff while performing the movement.
With these factors revealed, it shows that the use of rubber bands is limited to 1-joint being exercised. On the other hand, Flextend involves all 7-joints from the elbow to the DIP joint located near the tips of the fingers, making it quite obvious that there is no real comparison between the two methods of exercise. (Joints in Order from proximal to distal: Elbow, Radiocarpal (Wrist), Carpometacarpal, Intermetacarpal, Metacarpalphalangeal, Proximal Interphalangeal, and Distal Interphalangeal.)