Since the diameter of the probing convergent beam is smaller than in the case of a parallel beam, most of the information in the CBED pattern is obtained from very small regions, which other methods cannot reach. For example, in Selected Area Electron Diffraction (SAED), where a parallel beam illumination is used, the smallest area that can be selected is 0.5 µm at 100 kV, whereas in CBED, it is possible to go to areas smaller than 100 nm. Also, the amount of information that is obtained from a CBED pattern is larger than that from a SAED pattern.
Nonetheless, CBED also has its disadvantages. The focused probe may generate contamination, which can cause localized stresses. But this was more of a problem in the past, and now, with the high vacuum conditions, one should be able to probe a clean region of the specimen in minutes to hours. Another disadvantage is that the convergent beam may heat or damage the chosen region of the specimen. 
Since 1939, CBED has been mainly used to study thicker materials.