I think practically there is no standard, but 3db contours are pretty common. If you think about it , -6db isn't much, it certainly isn't like going from 'full output' to 'no output'. It's just significantly quieter.FWIW, with horns beamwidth is usually quoted as -6dB re on-axis. I'm not sure such a standard exists for cone drivers.
I think it's important to keep some perspective about the magnitude of off axis sound irregularities. If you look at the frequency response of a speaker off axis, it's going to be a bit darker, and possibly have a null due to crossover effects, but it's not going to sound dramatically, suddenly different; apart from anything else, the 'correct' axial sound becomes the indirect sound when you move off axis, and it will probably beautify the overall reverberant field.
This why I never liked the term 'beaming', directional effects are quite subtle and smoothly changing, and you never hear them in isolation.