To me constant is something like the 8c above 100Hz, controlled would be something like a Revel where the directivity is only controlled much higher up. Your description of yours sound like constant, just with different beam widths. A true omni would be constant.
The reason I was asking is it sound like you are saying low distortion constant directivity is clearly better than high distortion constant directivity, but that does not seem to be quite what Erin (and others) are comparing, as very few have probably done the comparison, they seem to be comparing low distortion controlled directivity speakers vs constant directivity but high distortion speakers, and saying they much prefer the latter, based on the speakers of both types they have so far heard. So that when it comes to real speakers you can buy and put in a lounge they will happily trade off a lot of distortion for a lot of directivity control, and without reference to something else don't hear the compromise.
The easy way to blind test this would surely be with low distortion speakers fed a mix of clean test tones, and distortion added test tones, no change of dispersion to engineer around.