About This Word, “Atheist” An "atheist" is a person who either "believes" there are no gods...or who "believes it is more likely that there are no gods than that there is at least one." — Frank Apisa
I think the definition of atheism “lacking belief in god” is the most sensible. This is accurate because all atheists lack a belief in god, it is the common denominator of the atheist category, and that makes it definitive of what an atheist is.
Contrasted to your own definition
“An "atheist" is a person who either "believes" there are no gods...or who "believes it is more likely that there are no gods than that there is at least one."
That Describes two kinds of atheists, two examples of people who lack a belief in god (one because they feel like they have some reason to believe no god exists, the other who lacks belief in god because they find that the more likely). It doesnt cover the ground it needs to in order to be definitive.
Your definition is the worse of the two, it confuses category and sub category. An analogy would be “berries”....you are defining “berry” as strawberrys and blue berries. Atheism is like “berry”, the guy that believes there are no gods is the “strawberry” and the guy thinking it more likely that there is no god the “blueberry”. An Agnostic could be a “raspberry”, just another berry (another type of person who lacks belief in god).
Aside from your aversion to the label, what makes your definition the better one? You havent demonstrated it at all.