I've never heard it with "way", bu
"six of one, a half-dozen of the other" (which makes sense as a donut order) is often (mis-)used to mean both options appear to be the same.

That's the point of the saying -- it means that two things are actually the same thing, there is no difference.

The phrase goes "6 of one, half dozen of the other"

And yes the whole meaning of it is that there's just a distinction without any difference.