It seems like it is free because the pre order doesn't have any paying!
Will probably make DayZ go down if it is good enough.
I doubt it. While the general setting and gameplay style would be pretty similar, they'll be different enough to be two different games.
It'd be like trying to compare Call of Duty to Counter-Strike. Sure, they're both FPS's with a lot of guns and team-based gamemodes, but they play so differently, and are two different games. You can still play and enjoy both games.
WarZ is going to be an MMO, pretty much making it a (personally) interesting combination of Dead Island and DayZ.
DayZ is just a sandbox. You're dropped in the middle of nowhere with no goal or directive, except for surviving. Lots of possibilities for player-to-player interactions that you're probably not going to get with WarZ.