To some extent I think this comes down to a preference, like many things in dithering. If the black and white results look good, that may be the right answer!
I've played with dithering tools that provide both options, and I prefer the output of the simple version..
Haha, yeah I was kind of thinking that as well! Like with different error-diffusion patterns, one method may be more visually appealing than the other.
Although, with either approach, I definitely feel that the fact that sRGB is non-linear should be acknowledged, and that’s something I was completely unaware of. So, I’m happy I learned something new today :)