I sometimes prefer parenthesis for very short asides—say, three words or fewer.
I find m-dashes easier to read for most other purposes. They’re nicer in longer asides because they’re a little more visually prominent, while also (for some reason) not breaking my mental flow quite so much. They’re far nicer looking when an aside comes at the end of a sentence, as you don’t need to close an m-dash. That always looks like crap with parenthesis, as if the author should have thought of a way to avoid doing that, while with the m-dash there’s no problem at all.
That is a weakness of sorts, but yes, unless one is attempting a particular, niche affect, an urge to nest parenthesis is usually a cue to re-write the sentence instead.
I find m-dashes easier to read for most other purposes. They’re nicer in longer asides because they’re a little more visually prominent, while also (for some reason) not breaking my mental flow quite so much. They’re far nicer looking when an aside comes at the end of a sentence, as you don’t need to close an m-dash. That always looks like crap with parenthesis, as if the author should have thought of a way to avoid doing that, while with the m-dash there’s no problem at all.