This topic is quite sensitive to moral and political views. The same question could be asked of Islam as it spread pretty successfully during the Arab conquest.

Ok, I guess I'll take a stab at this.

The circumstances that led to conversion to Christianity and Islam varied from culture to culture. However, when it comes to to losses of paganism, Alan Strathern has proposed a theory of transcendentalist intransigence: to quote "when faced with a dilemma of whether to undergo a wholesale conversion to a religion introduced from an external source, a ruler of a society shaped by established transcendentalist religion is more likely to resist converstion than a ruler of a society in which transcendentalist religion has had a superficial or negligible impact." (Strathern 2007: 359)

In his theory, a transcendentalist religion is characterized by an explicit and codified morality, a moral community voiced by or ventriloquized by a clergy, and an awareness of other religions and a readiness to meet them in metaphysical debate. Christianity, Islam, Buddhism, and to a lesser degree, Confucianism and Hinduism are such religions in his formulation. In societies strongly influenced by such religions, the moral elite (church, sangha, ulama, confucian literati, brahmans, etc.) would organize themselves to systematically resist the conversion of rulers and would support rivals to the throne when the ruler did convert.

It's is an interesting argument, and I haven't covered the whole thing; it's on jstor at http://www.jstor.org/stable/27563640. However, it has recieved substantial criticism in terms of its ability to explain events on the ground, and many societies converted for reasons other than their rulers converting.

To take a couple of case studies from the early modern period that I happen to have floating around...

in the Mughal Empire, "one means by which the populace was acquainted with the basic doctrines of islam was through folk poems" and worship at saints' tombs, as "people from all walks of life, both Hindu and Muslim, were attracted to the spiritual power... that was supposed to emanate form the sites where famous Sufis... were buried." Hence, over many generations, "segments of the Deccan population gradually came to adopt increasingly Islamic lifestyles." (Asher & Talbot, 2006: 168) In other words, in this context, the process of conversion was slow, diffuse, and a little muddled, at many points not being entirely one or the other.

in the Kingdom of the Kongo, the king who would become known as João I converted to Catholicism in 1491 and spread Christianity throughout the country, but the religion was rapidly "made a part of indigenous religion" and took on traditional functions such as "initiation ceremonies... providing individual charms for luck... protection of fields... public ceremonies to appeal to earth spirits in case of drought... consescrating the coronation of the king" and witch-hunting. (Thornton 1984: 157. jstor link http://www.jstor.org/stable/181386) In other words, Catholicism merged effectively with the social/religious/magical practices that already existed in the Kongo, which made the transition unusually seamless, but also points out the difficulties of evaluating conversion. Did the Kongo really convert to Christianity? People in the 1500's thought so, but by the 1800's the definition of Christianity had contracted, and the congolese were seen as basically pagan rather than basically Christian by new European missionaries, despite continuing their Christianized religious practices.

Other groups converted to Christianity becuase it provided a way of establishing legitimacy in opposition to the local state power structure. James C. Scott in the Art of Not Being Governed points out that this was a common response by state-resisting hill peoples in southeast asia to the arrival of Christian missionaries: it gave them new ideological resources with which to resist the incursion of valley states. This almost always lead to heavy syncretization, with Christianity being mixed in with all sorts of Buddhism, animism, Hinduism, and Confucianism to produce a mixture that worked well for the hill peoples. One could see the Taiping rebellion partially in this light, considering its syncretic origins and starting strengh amongst the Hakka minority in China's southwest.

So, to summarize, although there are generalized theories that propose that Christianity, Islam, and other religions like them (Buddhism, etc.) simply outcompete more localized pagan religions, the actual historical situations tend to indicate that the processes of conversion are complicated, often muddled and sometimes quite slow, rather than simple and clean and fast, that local pagan practices tend to be translated over into the new religious environment, sometimes almost wholesale, and that cultures were sometimes attracted to Christianity (or Islam or w/e) not because of what it was, but because of what it wasn't.

Hope that helps.