I don't think that morality, goodness, or kindness are innate traits. I believe that while we do have an innate capacity for these behaviors, we have a propensity to choose otherwise. Even when growing up as little kids, the first behaviors we learn are usually selfish, motivated by greed, or out of jealousy. We have to be taught to act kindly, to share, to seek after what is right. These concepts don't just "come to us" naturally.
But then again, there isn't really a good way of answering this when comparing people who have faith in God and people who don't. This is mostly due to the lack of common ground in defining what is "moral", what is "good", and what is "kind". Non-religious people usually aren't looking to God as the standard of what defines right and wrong, just as people seeking after God don't tend to just "go with what feels right" or "benefits the most people" or "makes people happy".
Someone who doesn't believe in God can be a good person. He/she might be generous, patient, kind, charitable, and gracious. But then again, there isn't any consistent basis for this. Another person who doesn't believe in God might well be a total creep and feel no compulsion to live otherwise. Taking a universal standard of morals out of the picture (ie: God) makes morality one person's opinion against another's. There isn't a definite "right" or "wrong", just relativism.
A nonbeliever's moral standard might occasionally line up with God's, but there isn't anything to anchor it there or provide a reason for why "good" is "good", etc.
On the other hand, those who follow God and hold him up as the standard of what is moral, just, good, etc., and what is not have a concrete basis for saying so. There's no room for a clash of personal opinion. Something either is good, or it isn't. But even people who love God don't always honor God with their words and actions. We're human too. But we know that such sin is wrong. That much isn't arguable. We believe that morality isn't up to man to decide because it comes from using God as the standard, not human opinion (which has, as I stated earlier, has a natural propensity to be self-serving).
Problems crop up when trying to bridge this "gap" in the definition of morals because there is no common, concrete standard of morals between those who believe in God and those who don't.