To me, brackets imply some kind of meta comment: a thought or remark that does not reside on the same level as the rest of the text and is therefore taken out of it:
Commas (don't confuse them with colons!) look like little Nines.
In fiction there is no meta level, where you, the author, speak to the reader. The narrator may address the reader, but this is still a fictional construct, a literary device, and takes place on the level of the narration. The author himself can only speak in a preface or afterword, or elsewhere outside the text of the novel.
Commas are just syntactic devices integrating adjunct clauses from the end of a sentence into its middle:
The ladder collapsed because it was old.
The ladder, because it was old, collapsed.
Dashes signify a break in the text and insert content from outside the chronological or argumentative order of the narration, e.g. a bit of backstory:
John — he was the oldest of Paul's three sons — did not hesitate to ...
You can convey the same information with commas:
John, the oldest of Paul's three sons, did not hesitate to ...
The difference, to me, is that with commas you just quickly provide the information while your story keeps running, while the dashes pause the story and take the reader for a short trip to another story, in this case the story of John's childhood. And even if the inserted clause only hints at that childhood, as in the preceding example, the dashes draw the reader's attention to this bit of information and signify its importance. You can, of course, provide more detail:
John — he was the oldest of Paul's three sons and had been beaten severely by his drunken father — did not hesitate to ...
That detour can be as long as you want, and you may repeat relevant parts of your surrounding sentence after the insertion:
John — he was the oldest of Paul's three sons and had been beaten severely whenever his father caught him gazing at his sister taking a shower through the bathroom keyhole —, John did not hesitate to ...