For the sake of completeness, in the comparing_hist_equalization_clahe.py script, you can see how both CLAHE and histogram equalization (cv2.equalizeHist()) work on the same image, visualizing both the resulting image and the resulting histogram.
This can be seen in the following screenshot:
It is safe to say that CLAHE gives better results and performance than applying histogram equalization in many situations. In this sense, CLAHE is commonly used as the first step in many computer vision applications (for example, face processing, among others).
