Luke Galen, an associate professor at Grand Valley State University, has released the results of his Non-Religious Identification Survey, which he conducted in partnership with the Center for Inquiry.
This is apparently the first survey to look for meaningful distinctions within the nonreligious portion of society, such as differences in upbringing, emotional stability, and how they choose to label themselves (“atheist,” “agnostic,” “spiritual,” “humanist”). Past studies comparing believers and nonbelievers have tended to lump together the nonreligious as if they’re one homogeneous group.
The chart above summarizes some of the results. It appears that confident nonbelievers (“atheists”) are more emotionally healthy than “fence sitters” and religious doubters—though tentative nonbelievers tend to place greater emphasis on being agreeable and trusting others.
There are also some other differences among nonbelievers, as Galen writes:

In regard to personality, the four main types of self-labeled nonbelievers differed not in openness to experience (which is more of a distinguishing characteristic between believers and the nonreligious) but on two other Big Five personality dimensions: the aforementioned agreeableness and neuroticism (that is, negative emotionality). In personality terms, spirituals are more agreeable than are humanists, who are in turn more agreeable than atheists and agnostics. However, spirituals also report more negative emotionality (i.e., are less emotionally stable) than atheists and humanists, who are relatively more stable. … The agreeableness differences may indicate a certain willingness among the spirituals to try to “get along with” or trust others (as mentioned above, they report having more close confidants) in contrast to the atheists, who display relatively greater willingness to go against the social grain. One can debate whether or not this confirms or disconfirms the “angry loner atheist” stereotype.

Keep in mind, however, that Galen’s sample of nonbelievers is skewed toward those who are actively involved with secular issues or groups (an email request for participation was sent to members of the Center for Inquiry Transnational), so it’s not necessarily representative of the nonreligious population as a whole.