The basic plot is the same in each — survivors of a zombie apocalypse try to continue to survive. Zone One, however, takes place over three days in New York City at the supposed tail end of the plague, as main-character Mark Spitz and his three-person "sweeper" crew go building-by-building to clear out the remaining "skels" in an attempt to make lower Manhattan re-habitable.
The schtick for Zone One, as you may have heard, is that it's a "literary" zombie novel. Just as Zombieland was a new take on the traditional zombie apocalypse story, so is Whitehead's novel an attempt to break out of the genre's convention. He does so with incredibly detailed, metaphor-laden sentences and paragraphs, constant flashbacks, and digressions inside of digressions. It's all very disorienting. And not always fun.
Put it this way: It's not a novel everyone will enjoy. But even if you don't enjoy the novel as a whole, there are several set pieces (a flashback to Mark Spitz and some friends holed up in a farmhouse, the story behind how our Mark Spitz came to be known as Mark Spitz) that are absolutely dazzling. And the last 30 pages or so scream by at a pace approximately triple that of any 30-page stretch in the rest of the novel. So even though it's a difficult novel to engage with — you have to really be in the mood to read diligently — I'd still recommend checking it out.
Whitehead is an amazingly skillful writer. As one of the back blurbs states, "Whitehead has a David Foster Wallace-esque knack for punctuating meticulously figurative constructions with deadpan slacker wit..." Agreed. Whole-heartedly.