A good study of especially the neo Stoics is healthy for anyone, and there was an awful lot that they wrote that the Church Fathers were in deep agreement with, so much so that Dante placed Seneca in the first circle of Hell, which is about as good as he could get. Stoicism has led many very intellectual persons to Catholicism, as with Leah Libresco.
The elements in which neo Stoicism differs most profoundly from Christianity are illuminating.
1) Think about how the Stoics look on love, and see if you agree with it; at the very least, they see it as toxic to self-sufficiency. Contrast it with especially St. Paul's writing on the topic.
2) Consider the goal of self control, which both the Stoics and the Christian ascetics considered a primary goal. Is the best end to master oneself, or to renounce the self?
3) Relatedly, the Stoics see self sufficiency as a virtue ("The wise man is self-sufficient"), but at the same time they share the ascetics' perspective on inherent depravity. The Christians of course see the self as insufficient and external salvation as necessary. Does the first perspective lead one to nihilism? Are people usually able to overcome their nature by themselves?
Good stuff to think about.