For me that argument goes like this:
1. If the God of Christianity exists, then sincere Christians would be significantly morally better than everyone else.
2. Sincere Christians are not significantly morally better than everyone else.
3. Therefore, the God of Christianity does not exist.
The argument itself springs from a question. If the God of Christianity exists, then why aren't Christians better people? This is of course not to say that Christians are bad people. It is to say that morally speaking, they are not noticeably different from people of other faith traditions and people of no faith at all. The spiritual transformation of individuals resulting in people who are more loving towards God and others seems to be an essential part of the Christian message. So why don't we see it?
A common response to this line of inquiry is the "user error" response. God desires for people to be more loving, but people because of their free will, disobey and remain in a state of moral mediocrity. There's some merit to this response, but it seems ultimately dissatisfying. Surely there are at least a significant minority of self-identifying Christians who sincerely desire to be more loving and to pattern their behavior after Jesus Christ. Why does it seem that most of these individuals ultimately fail to develop the kind of character that others would immediately identify as being Christlike? Second, in most Christian theology, transformation character is primarily attributed to the Holy Spirit. If this is the case, then the user error response seems misguided. If God is ultimately responsible for character transformation, and there are sincere Christians who make informed attempts at initiating this transformation, then where are the Christlike Christians? This is even more troubling if you adhere to a Reformed theology. If God has already chosen who's going to heaven, then why doesn't he go ahead and choose to make them into selflessly loving individuals?
Perhaps the second premise is false. This premise is an empirical claim. Of course, I can only speak from my own observations. I have met and am friends with many Christians who are good people. But, they really aren't noticeably more loving or charitable than people whom I've met who are atheists, Muslims, Jews, Buddhists, Wiccans, etc. Perhaps someone out there can point me to some data showing Christians to be noticeably more loving than others.
Ultimately I don't think that this argument is sound. But, it's very compelling, and I don't have a good objection to it.