21st Century Dead: A Zombie Anthology, edited by Christopher Golden, goes for the second option, which I think was the right choice. There are about three (or maybe four) stories in the anthology that I wouldn't classify as having actual zombies in them. The rest do have zombies in them, though they aren't all flesh eaters and they aren't always central to the story. I generally enjoyed the stories in the collection. To break things down, there was one story I hated, one story I loved, one story I kind of disliked, and sixteen stories that I liked to one degree or another.
The story I hated was "The Dead of Dromore," by Ken Bruen. I actively disliked the characters in this one, who are a band of mercenaries paid to go into a zombie-infested town to rescue a survivor, and who would rather murder all of the other survivors than rescue them for free. Disliking the characters isn't usually enough to get me to dislike the story itself, but the style was. It has way to many sentence fragments and short sentences for my taste. Plus there's a lot of weird formatting where single sentences are broken up to be spread across several paragraphs, looking something like this:
Helped there by a combination of
And the Chinese
Spreading a single sentence over four paragraphs is just annoying. If I thought it was just a product of my copy being an ARC, I could overlook it, but I suspect that it is intentional.
The story I loved was "Ghost Dog & Pup," by Thomas E Sniegoski, which was one of the less zombie-centric stories. There are zombies in it, but they don't really show up until nearly the end and aren't the focus. At its heart, I would call this one a boy and his dog/ghost story. I suspect the reason I enjoyed it so much is because, being a dog lover, I've always been a sucker for boy and his dog stories.
The story I kind of disliked was "Tic Boom, A Love Story," by Kurt Sutter. In this case, the story was interesting, but as with the story I hated, the style annoyed me. Kurt Sutter is the creator of Sons of Anarchy, and this is his first piece of published prose. As such, it isn't surprising that his story reads more like a screenplay than a short story. It doesn't make the story bad, but it did distract me a bit too much.
Since this review is getting a bit long, I'll just briefly go over the other stories that stood out to me. I really enjoyed Brian Keene's "Couch Potato" and Jonathan Maberry's "Jack And Jill," which isn't surprising as those are two writers I really enjoy. Despite finding his politics abhorrent, and his tale not being an actual zombie story, Orson Scott Card's ""Carousel" was a good story. Chelsea Cain's "Why Mothers Let Their Babies Watch Television" was pretty funny. "Tender As Teeth," by Stephanie Crawford and Diane Swierczynski, was interesting because it was about a person who'd been cured of zombieism.
Despite having a couple of stories I didn't like, this was a good anthology that I recommend for the zombie lover.