Imagine an illiterate peasant in the Middle Ages who claims that he believes in Jesus Christ, but because he can't read or write, he requires the priest to read the Holy Scriptures for him. Now, the priest is corrupt and intentionally misreads the Bible for his own gains: to control the life of the peasant.
Imagine an irreligious person in the modern age who claims that he does not believe in Jesus Christ, but instead focuses on reading the Holy Scriptures and talking with Christian friends to learn more about Christianity and the Bible. He remains irreligious, though.
I don't really think the two concepts presented are like for like. It's like asking which is better, eating healthy or visiting family on vacation. The one is not like the other and thus they aren't measurable against the other.
In the former case, "faith in Jesus Christ", that is important (speaking from a Christian POV) because our trust in Him--even if we be illiterate, uneducated, or whateverhaveyou means that we are found in Him, who is now saving and redeeming us.
In the latter case, "knowledge about the Bible and Christianity", that is important (speaking from a Christian POV) because it is important to have an examined faith, to be able to articulate and comprehend the robustness of the Christian faith and not be ignorant about what it is that we--as Christians--confess and believe.
For the one who is without faith, I'd like it that they try and understand Christians and our Christianity when they engage us in conversation; principally because it is frustrating for anyone if and when someone imagines what it is you ("general"
you) believe, confess, and/or think.
I don't think there should be a choice between the two, I think preferably the two go hand-in-hand. A Christian who believes, but is unwilling to learn about their religious faith, does for themselves no good service; someone who has a working knowledge of Christian teaching, practice, etc, but is without faith, robs themselves of the divine life found in Christ available for and to all.
-CryptoLutheran