The short answer is that the "throw" of the horn depends on the geometry of the horn that is loading the driver. Whether of a constant-directivity type, exponential, conical, or some computer designed thing in between, they all take the total acoustical power of the driver and disperse it in some defined pattern. I once bought a Renkus-Heinz constant directivity horn, bolted it up to a driver and measured its on-axis response. Because the response of the driver was flat, I was expecting the response of the horn & driver to be flat with frequency. It was not. In fact, the response reduced as the frequency increased. I thought something was dreadfully wrong until I realized that because it was a constant-directivity type, the acoustical power was distributed to create the constant-directivity pattern. There was a fall off in response, but the fall off was the same off-axis as on. An exponential horn response would have been flat on-axis but would have fallen quickly off-axis. BTW, the fall-off in response with frequency was easily compensated by EQ.
I guess that wasn't a short answer after all. 😜