Haven't played rust, so cannot form a balanced opinion. However, I have watched a lot of gameplay on it and it does look like a lot of fun. I probably will buy it at some point.
In my opinion, DayZ, even in its current state is probably better, because I think it has more scope; there's a lot more to it than just killing fresh spawns and running north. Even now, in the early builds, there is tons more player interaction than seemed to occur in the mod, and hopefully they will never add OP weapons like .50 snipers, etc. and thus maintain player interaction. I really like the Zombie Apocalypse concept, and I think DayZ brings us about as close as we can get to that. It's not the only game in the genre, but it is the best if you want a 1st/3rd person immersive zombie survival game.
And on the flip side, - not saying that Rust is bad in what it delivers, but it's not the 'only' game that is satisfying the 'survive and build' genre at the moment. In fact that genre is pretty much dominated by Minecraft. In fact the Devs even said it was inspired by a combination of Minecraft and DayZ.
Just thought I'd chuck my opinions in given the fact for the last two pages this has become a rust thread! XD
