While I generally avoid generalizations (^^), there may be reasonnable grounds to hold that view, the accuracy and relevance of which depends on a primary factor: who are Atheists?
As per the name, one could be Taoist, satanist, or a member of one of many other religions, which may not have a god, but do have spiritual beliefs ( some may even argue that nationalism, capitalism and other such constructs may well be atheistic religions). In which case, I feel the answer would be no, I would see no reason to differentiate between the level of introspective and self-analytical capacities of any socio-religious groups, at least not without significant imperical study in the matter.
But I suspect these may not be the "atheists" you were refering to in your question. Western understanding of atheists has changes significantly in recent times, and one could understandably have growned to confuse, or use interchangeably, the term to identify individuals with purely naturalistic world views.
If that were to be the case, my answer would be yes, as these individuals make for over 80% ( and I'm being intentionnally conservative as I couldn't be bothered to find the statistic) of the scientific and research community of the world. Evidence would seem to point towards there being a link ( as correlation for causation, I can only guess.) between one's degree of skepticism in the face of the supernatural and one's ability for reflection and critical thinking, and one may dare say, intelligence and relevance.
I think that atheists are calmer and more level-headed than
religious people. Most of the wars in
recorded history have been started because of religion. Religion tends to blind people’s judgment and
make them think that they are always right.
Atheists may be heartless, amoral scum, but they are generally rational.
Like with any religious group, there can be extremist atheists who push their beliefs onto people. Like some atheists, there can be religious people who are happy to just believe in what they believe in and not worry about what anyone else says or push their beliefs onto anyone. As has been previously mentioned, it all depends on the person and whether or not they are calm and level-headed or not.
This is really something you can't generalize about. If you've ever gone on the atheist discussion board on Reddit, you'll see some stark raving loonies that rival the most unbalanced Christian fundamentalist you could imagine. And if you go on the Christianity board, you might see a lot of calm and level discussion. In the end, it's about the individual.
I do not believe there is any way to say that all atheists are calmer and more level-headed than religious people. Not all people who are atheists are calm or level-headed, they've just come to the conclusions that they have. Again, there's nothing to say that a religious person couldn't be calm and level-headed. This questions is so distasteful and biased.
You'll find hard-headed, disagreeable people on both sides of the spectrum. Many atheists are extremely vocal, loud-mouthed, and anti-religious, just as many Christians are fundamentalists, close-minded, and hateful. There are also people on both sides who have a live and let live attitude and get along with each other just fine.
I think it really depends on the person not the religion or lack of when it comes to how calm and level headed someone is. Atheists would be calm in the sense they will not be trying to convert people to a religion because they don't have one, but that doesn't mean they aren't trying to get others to believe or not believe how they do.