Source: Philip Schaff, History of the Christian Church, Volume II: Ante-Nicene Christianity (Grand Rapids: William B. Eerdmans, 1910) 22.
"But the fact that the Christians were a closely united body, fresh, vigorous, hopeful, and daily increasing, while the heathen were for the most part a loose aggregation, daily diminishing, made the true prospective strength of the church much greater."
Schaff is addressing the question of how Christianity grew so quickly in the first three centuries C.E. Most of the time, he gets into preaching mode: Christianity grew because of its miracles, or because of its inherent beauty as a belief system. I'm not going to rule out those explanations, since the New Testament attests to the power of miracles in bringing people to Christ. But there were others who did miracles in those days, plus the beauty of a belief system is in the eye of the beholder. So why was Christianity so special?
Liberal scholars like to argue that Christianity borrowed its beliefs from other religions: mystery religions, paganism, etc., etc. But why did Christianity grow so rapidly, if people could easily get the same sorts of beliefs in another creed?
Some have argued that Gentiles liked Judaism, but they joined Christianity because it lacked Judaism's painful circumcision requirement. But, as Krister Stendahl has pointed out, that doesn't exactly match what we see in the New Testament. Galatians makes clear that there were Gentiles who actually wanted to be circumcised and keep the law. According to Stendahl, this was because Gentiles were drawn to the mysterious customs of the orient. So why did they become Christians and not Jews? I don't know.
What I like about the Schaff quote is not that it satisfactorily answers the question, but that it may give us a lead. Why did Christianity grow, whereas other religions with similar beliefs did not? Maybe because Christianity was an active, organized movement that sought converts, something which was not really true of travelling miracle-workers, mystery religions, and Judaism.