There are different kinds of breathing - deep or shallow. relaxed or with abdominal tension. quick or slow. Which kind is best? I think it depends on the purpose of the breath. In combat, the purpose is to facilitate the technique. Different techniques require a different kind of breath. As a general rule faster action requires faster breathing, grappling against resistance/weight is enabled by slower breathing with abdominal tension (to provide a solid base/fulcrum), and during a lull in the action it can be slow and deep. In this respect Wing Woo Gar has the order correct IMO.
(He used "motion creates the breath" but I used a slightly different "motion determines the breath." I just thought that "determines' reflects more deliberate purpose/intent as opposed to a spontaneous "creation." A small but perhaps significant difference in connotation. But the important point is that breath reflects motion rather than visa versa. Kind of the chicken and egg thing.)
A different category is exercise where the purpose is to develop "internal" development. Sanchin kata, for example, uses slow tension breathing, even in the punches - not practical in fighting but it helps develop certain structural factors. This view seems to me to be more prevalent in CMA, but what do I know? An interesting side note: When goju founder Miyagi's teacher, Higaonna, brought sanchin from China to Okinawa it employed fast punching without dynamic tension in the technique or breathing. Miyagi changed it to the version commonly seen today, although Uechi-ryu uses the fast punching (with spear hands) and quick sharp breaths.