The best way to look at it would be the quality of the Sound Power curve. Whether it is Active, Passive, or omnidirectional will only matter in so far as it can aid in making a better Sound Power curve. The Directivity Index is essentially the inverse of the Sound Power so a good Sound Power means a good Directivity Index too. Unfortunately, Sound Power data is very difficult to get on loudspeakers as it is generally never measured, likely because you require an anechoic chamber to measure it and it is a lengthy process to measure and calculate. In the design process getting a linear on-axis and Listening Window is pretty straightforward. But getting a nice Sound Power as well is a lot of work.
