I read the 1966 edition, and these comments apply specifically to that edition.
Literature by its very nature is open-ended and difficult to organize in a truly systematic or conclusive way. You can classify literary writings by culture of origin, historical period, or movement, e.g. Romanticism; yet each work is entirely individual and has something unique to say that cannot be subsumed under any classificatory heading.
The editors of this anthology made the choice of *voice* to organize their selections. From what and whose point of view does the author unravel his or her story? This volume offers one relatively concrete way to approach fiction reading and make it fit a bit more tidily into a curriculum of more easily systematized subjects, like chemistry, statistics, even foreign language learning. Yet "point of view" is only the take-off point. The real value in good literature, of which these stories are outstanding representative examples, is the story, the message, the language, all of which leave technical issues behind in a cloud of dust once you are drawn in to the author's world.
This is probably the best collection of short stories in English I have read. Each one of the stories cuts to the quick on themes of love, hate, separation, reunion, guilt, and death. Some are by familiar authors, who I'd first read in junior high school, others were completely new to me. At no point was I reading just to finish the book; I savored each work. My favorites include pieces by Dorothy Parker, Fyodor Dostoevski, Daniel Keyes, Cynthia Rich (sister of Adrienne), Frank O'Conner, Jean Stafford, Guy de Maupassant, and Saul Bellow. I was surprised and deeply impressed by John Steinbeck's "Johnny Bear", which I hadn't known of before, and now plan to use it in my freshman English class. Even the story by DH Lawrence, who I'm generally not that crazy about, was an excellent choice. The story by Moffett, one of the editors of the collection, is engaging and skillfully written. I was moved rereading Keyes's "Flowers for Algernon" in a way I don't remember feeling when I first read it for a class decades ago.
I'm a bit disappointed at some of the swaps made for the new edition, e.g. the Dorothy Parker. The Ambrose Bierce, on the other hand, could have been replaced by something with broader appeal. I thought some of the stories might have been omitted due to concerns of political correctness, but "Powerhouse", "The Iliad of Sandy Bar" and "The Suicides of Private Greaves" are, thankfully, still included. Personally, I recommend ordering a used copy of the original edition for a consistent picture of the editors' original vision. It is a coherent one, and I can't imagine that coherence was completely preserved in the new edition - though I'm sure it is also a strong, but quite different, collection.
These stories bear out the words of past Bridport Prize judge Martin Booth: "A short story is like a slap in the face. It must immediately sting, make itself known at once, and it must leave a red mark for hours to come." Each one of these stories does just that, to the point that you need recovery time after each one to get over what you've just been "slapped" with, and to ready yourself for the next blow. Highly recommended.