The obvious answer is that there's no direct correlation between quality of life and believing in God.
This reminds me of a study that was performed by Pew (I think) a year or two ago. It was measuring happiness levels and religiosity.
What was interesting is when the study was performed in the USA, they found a positive correlation between whether or not one was religious and how happy they were. It did, at least initially, seem to give credence to the notion that being more religious does make one more happy.
However, they then performed a similar set of studies in countries that are known to be far less religious. Like Sweden or the Netherlands. And interestingly enough, they found the exact
opposite correlation. People who identified as less religious seemed to be more more happy in those regions.
What it seemed to ultimately dictate, at least to a certain degree, is that the happiness component seemed to be more positively correlated with a feeling of being more in line with the status quo and feeling like one was part of the general community. So in places where religion is more dominant, people are happier associating with that religion or its institutions for want of fitting in. Likewise, in areas where the status quo is one where there is less general religiosity, happiness there was demonstrated by the non-religious.
So happiness in a certain sense is more correlated with that of conformity than anything else. Fitting in and feeling like you are part of a broader social group is something that generally aligns with higher levels of happiness in humans. Which I guess makes sense since we are a social animal.