I recall we examined this thesis when I was in college, but I haven't got anything insightful to say about it just now. However, this two-part division of culture is interesting to me for another reason, and it is one expressed by Matthew Arnold in his Culture and Anarchy, in a section on Hebraism and Hellenism. Here he revisits Tertullian's ancient question: What has Athens to do with Jerusalem? And I only just now noticed that in doing so he makes an allusion to Lucretius;
QuoteTo a world stricken with moral enervation Christianity offered its spectacle of an inspired self-sacrifice; to men who refused themselves nothing, it showed one who refused himself everything; — "my Saviour banished joy" says George Herbert. When the alma Venus, the life-giving and joy-giving power of nature, so fondly cherished by the Pagan world, could not save her followers from self- dissatisfaction and ennui, the severe words of the apostle came bracingly and refreshingly: "Let no man deceive you with vain words, for because of these things cometh the wrath of God upon the children of disobedience".
Nietzsche it seems will have resented much of what Arnold panegyrized, but I will have to review The Birth of Tragedy before saying too much about the Apollonian and the Dionysian.