... who is the better person: the atheist who does good deeds just so or the religious person who only does good to win favour with GOD ...?
I think that this paragraph highlights the problem that Christianity faces. ALL other faiths are based on the concept of 'doing good to win favour with God', so it is assumed by many people that this is the case with Christianity. Like your questioner, I would tend to doubt the sincerity of those who do good to win favour (and it doesn't actually have to be 'with God') so that this charge can laid at the feet of atheists as well.
Your questioner provides a false duality, where there ought to be a trinity, since Christians will usually 'do good' as a response to God's offer of salvation, rather than as a means of winning favour with Him.
And I think this paragraph highlights the gap between discussion of religious metaphors and human psychology.
Obviously people do good to others out of compassion - it is very difficult to ignore another's plight - it's a natural instinct and there is neurological evidence that compassion is hardwired - see recent discussions on mirror neurons in the literature of neuroscientists - religion is a cultural metaphor developed through the ages as a narrative for making sense of things we don't know about yet.
