Both and neither.
For myself, I was much less happy and content when I was trying to believe in a higher power (key word is *trying*, because a monotheistic god (at the very least) has never made sense to me on a variety of levels and I'm basically incapable of doing the Faith thing). It was impossible for me to reconcile the actual world and universe around me with religious teachings, and the inconsistencies of so many things drove me batty. None of it made sense and it was starting to eat me alive. So to speak. In essence the 'Worldview'/perception I would have had to have to maintain a belief in god/religion was in total opposition to what I saw/thought/concluded/observed/studied/etc.
Once I went through the process of sorting through my own view of things, which, in essence, is of more of an atheistic bent, I have had much greater happiness and peace than I had EVER had while trying to adhere to and believe in a religion.
But as many others have already said, it greatly depends on the person and his own disposition. It's clear that a great number of people are much happier with their beliefs in a religion/god than they would be without.
Also, the psychological challenges/inconsistencies one with strong faith encounters will be totally different from the challenges one without faith encounters. Both might be equally 'hard' - just by nature different. I also think you'll find profoundly happy people who are at peace while holding to a faith, profoundly happy people who are at peace while being atheistic, profoundly unhappy of both, and everything possible in between and within.