It's definitely not a clone of ATZ. ATZ is more a RPG lite, with a heavy emphasis on solitaire play. Last Days is more like Necromunda, with the added fun of zombies. Before their turns, players alternate activating a zombie until all the zombies on the table have been moved. The zombies don't move randomly – you move them to inflict maximum annoyance and damage on your opponent.
The focus in ATZ is survival. The focus in Last Days is more like the Walking Dead show – other human groups are the primary enemy.
Besides being somewhat like a gang fight, Last Days is also like Necromunda in that it is designed as a campaign game. There are a number of scenarios. After each battle, your people get experience, advance, scavenge, that sort of thing. It is definitely not suited to solo play (unless you think Necromunda is good solo game).
And I'm using Necromunda to describe the play style, not the rule mechanisms themselves. LD rules are fairly straightforward, but they seem clean and simple with the caveat I haven't played it yet myself, just read through it. The keywords, as Jacob said, are for force composition, so that the force you choose can be – if I may use Walking Dead archetypes – like the Saviors, or Rick's group or Hilltop, or the Junkyard people.
Also, and I find this quite unusual a Osprey hardback book, it is quite well organized. (I've found most Osprey hardback rules, like Force on Force, or Tomorrow's War, or Field of Glory, to be poorly organized). I found it easier to read and digest than ATZ to be honest.