It really depends on the design and the designer.
Most tweeters are at least 1" diameter to maintain the efficiency (actually sensitivity) required to be "accepted". At that size, they will beam at 13.5kHz and above (wavelength of sound at sea level about 1"). Then, they are modified by horn loading, phase plugs, boundary effects, baffle, etc.
Soft/hard domes/cones do not make much of a difference in this radiation pattern.... only in the resonance frequency of the dome/cone. Then, as this "oil can resonance" is usually quite a bit above 13.5kHz depending on the cone material and mass, you only hear it when the tweeter points directly at your ear. Soft domes distribute this resonance and the resonance pattern is different - not one single frequency.
The various designs of ribbon tweeters have a different problem. When they are long enough to have high sensitivity, they have a string resonance that depends on the mass, tension and length of the string. They also become effectively a line source and the radiation pattern may be wide horizontally to an extremely high frequency (depending on the width of the line-source) but vertically there may be no dispersion at all (modified by wave guides, etc.). Other designs of ribbon or planar magnetic type tweeters (including mine) have chaotic diaphragm behavior that needs to be heroically managed.
A compression driver behind a horn may be the perfect tweeter - 1/4" diameter, with a horn to amplify. A plasma tweeter amplified by a horn IS the perfect point source tweeter - almost zero mass, almost zero dimensions. But the sound of a horn driver (to my ears anyway) is quite disturbing - I'm just saying that I do not prefer it with no mention of absolute sound quality.
There is no one right way to position any loudspeaker irregardless of design. Follow the recommendations of the loudspeaker designer, and then adjust to taste.
If you read specifications and charts and graphs, and find the loudspeaker with the flattest frequency response on axis, buy it and bring it home, at the listening seat you'll probably never have it exactly on axis to your ear. When you are listening perfectly on axis, then 1/2" makes a big difference. You'll need to have a clamp for your head mounted on the listening chair. Just saying.......
