It depends on the shape of the horn. If it is a purely conical straight horn, then the directivity will match the horn flare up to the point where the wavelength roughly equals the diameter of the throat and down to the point where wavelength approximately equals the diameter of the mouth. At the upper point, directivity of a circular radiator narrows to about 90°, so if the flare angle is narrower, it will still set the pattern. Phase plugs raise the useable frequency too. So basically, a 1" exit driver with its 2" diaphragm and phase plug is not going to beam anywhere in its bandwidth as a result of the driver. It's the horn that will set directivity.Horn shape is what you should focus on, and part of that is contained in the driver. The first part of the expansion is inside the driver itself, and it is usually a conical expansion with very little flare, almost a straight pipe. That will cause narrow directivity at very high frequencies. Bolt-on drivers are usually shorter than thread-on drivers. In either case, the beginning expansion of the horn is contained inside the driver. And then there is the horn shape that you can see. If it has a curved shape, then directivity will collapse with frequency as a result of the horn. That's designed-in beaming, used to provide acoustic EQ at the expense of polar response.
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