I'm currently running the Azenis on my car and I daily drive it year round. I had the DZ1 before on a turbo Miata, so the comparisons are a little moot.
Compared to the stock tires these are worlds better and the car really comes a live. The inside/outside tread pattern also makes for more options for rotating tires compared to the DZ1 before.
I would say the tires handle pretty good in the wet, but as someone else has said, standing water should be avoided (though that's true for pretty much any summer performance tire)
To me the Azenis is a great balance between a dedicated track tire like the R888 and other so called "high performance summer" tires. Once I started driving on tires like the DZ1, AD08R (have them on a Golf R), and Azenis I could never go back to harder tires!