DayZ is a survival simulator with a lot of PvP and a few zombies thrown in. Good at what it aims to do, maybe the best, but it's not really a zombie game. I haven't fully experienced it, but from the countless YouTube videos I've seen, it's a lot more fun with friends and mics.
State of Decay is a group survival "casual simulator" with more focus on zombies. There are a lot of different zombie types and they are a big threat. There are multiple different characters that all work together, and you can play as most of them. It also has story missions. You can also clear buildings, find supplies, and build new things. It might overstay its welcome by getting repetitive after a while but if you buy it on sale you can probably play it, beat it, and get your money's worth before it becomes aggravating.