While they are the same game, they're different as well. Day Z was more about exploration, actual survival, and scrounging around for spare parts and things like that. There's even some awesome servers now that have full RP rules and are enforced, so people can get kidnapped, certain sectors of the map are controlled by gangs, open trade. It's pretty awesome. WarZ on the other hand is more of an Action FPS game with some minor nuisances from the NPC's. They could completely get rid of the Zombies and just have full PVP and it'd be pretty much the exact thing.
As which one I prefer, I personally HATED WarZ. The game was awful, it took far to long to give players the 'Promised' content, in which they still haven't released any other map besides the first one. (We're supposed to have 3 of them.) and the combat is pretty mediocre. DayZ was great because it was still ArmA which came with it's own flaws, but the map size, player limit, exploration, and just the grand scheme of things was awesome. Finding a helicopter and taking to the skies to call out a camp, mark it down, then attack it at night fall was beautiful