It's not a question of whether Christians are better people or not. It's a question of forgiveness of those bad things, and the response to that forgiveness.
Someone who is not religious may do something bad, but there is only his or her conscience to catch them out. Even then, there is no reason to obey the conscience except if another person catches them out. The craftier a non-religious person, the more they can get away with if they choose.
Now, I'm not saying that all non-religious people will try and get away with everything they can, but there is no good reason not too in their eyes. If you are non-religious and have a reason to do good, you have to show that there is an objective 'good' and that your reason to do good is worthwhile.
Someone who is a Christian receives forgiveness for their sin, Christ taking punishment on the cross for them. Their response to this should be gratitude, leading to a greater reluctance to do wrong in the future. This means that someone who is a Christian (and not a pretender - there are many) will become a better member of society over time.
Eternally speaking, the biggie is Judgement Day. The difference between a Christian and non-Christian on this day is forgiveness and heaven (eternal life) and un-forgiveness and hell (eternal death).