If you define "better" solely by precision, then the Kinect is better.
The Wii relies on a combination of the Wiimote and the Balance Board for various exercises. With the remotes, the system uses infrared lights and accelerometers in the remote to figure out where your hands are and in what direction they are moving. With the Balance Board, it can figure out how you are shifting your weight around via pressure plates.
The Kinect operates by sending thousands of infrared rays of light across the room. The camera is able to figure out the shape of everything in the room based on how far a beam of light travels before it hits something. Because of this, the Kinect is able to determine a full outline of the person using the system as well as how every part of the body is moving.
Because of the above, the Kinect is more aware of your entire body and what you are doing with it than the Wii peripherals are capable of being.
One advantage the Wii solution has to the Kinect, however, is that the Balance board can weigh users. This allows the system to help measure progress automatically without the need of weighing yourself on another scale. The result is that the Wii is better at tracking your overall progress in terms of weight loss.
Of course, you can easily compensate for this deficiency in the Kinect by purchasing a scale. You cannot really compensate for the decreased lack of precision in the Wii, however.