Is an average non-religious person more likely to be more moral than average religious person?

More or less religious is a bit ambiguous.

What I've experienced... the religious that allow their religion to determine their morality (derive their morality from their religion) appear to be more prone to amoral behavior than the religious that have integrated the morals of their religion and those of their own moral intuition.

I sense the moral intuition, or an innate concept of morality is the defining factor... not necessarily one's religion. There are religious individuals that can understand the reasoning and concept of 'Do unto others..." and there are those that- "Well, I better 'Do unto others' or god'll be mad at me."