This friend of mine is one of the kindest and respectable human beings I have come to know. I can honestly state that he, in my opinion, is more moral than many Christians I know. I'd go as far as throwing myself into the mix.
The simple answer to this question is "No". There is not a single action that a moral atheist is incapable of making compared to the moral Christian. However, if we attempt to answer this question, we are missing the point of Christianity.
For some, being Christian means to make sure you're baptized and meet the pre-requisites (whatever they may be, faith... works... sacraments...) to get to heaven. I don't believe any of these to be true either... the whole faith vs. works argument assumes that salvation is something that can be objectified. You either have it or you don't. To the Orthodox however (correct me if I'm wrong), salvation is not something we can claim we "have"... rather it is man's ability to respond to the love of God. We are always gravitating toward Him, becoming by grace what He is by nature. If we are to objectify salvation, then we can claim to either have it or not. If indeed we are "saved" (notice the past tense), then what current need of a Savior, since we are already saved?
Why did my friend get the impression that we as Christians claim to have a higher morality than he? If anything, it's our lack of morality, or rather, our fallen nature that calls us to NEED Christ. Christ taught us that the greatest commandment is to love God with all our heart, soul and mind... the second greatest commandment was to love each other in the same regard. Nowadays however, Christians have turned to be judgmental and resorted to condemning those who are not believers. Where is the humble quality of Christianity nowadays? Why is it when a non-believer looks at us, they feel an egotism that is not characteristic of Christ's message of love? Many Christian denominations, condemn those who don't believe in Christ. Because they are not "justified" by the Blood of Christ, they remain sinners and are going to hell. This condemnation affects both parties. The condemnERS have a tendency to sound egotistical (sometimes are) and superior, the condemnED feel ashamed, insulted and belittled.
We as Christians need to see ourselves for what we are, fallen and sinful. The difference between a non-believer and believer is the truth of Christ, not simply the moral standard by which we live. In other words, Christians should never claim to be "more moral" (moraller?) than non-Christians AND we should make sure that the image we bear of Christ is not bereft of love.