Chief Rabbi Leon Ashkenazi said: "The difference between an atheist Christian and an atheist Jew is that an atheist Christian does not believe that God exists, while an atheist Jew believes that God does not exist."
I'm not so sure about the Jewish-Christian borderline, but I love the nuance.
So which sentence suits you better?
"I don't believe that God exists."
or
"I believe that God does not exist."
And... why?