... 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.