A few answers come to mind. The main issue here is distinguishing Catholicism from other forms of Christianity. This is a major issue in earlier on, and less of one as time continues.

A first answer is that Christianity was an appealing ideology to many persons excluded from the religions that dominated in their region. A religion that promised equality and universalism was, and is, attractive to those who are either tacitly or explicitly excluded from the dominant rites and celebrations of their community. This reason partially accounts for the success of Christianity among women and slaves in late antiquity, who were excluded by either gender or legal status from taking place in the legal and celebratory rites of their political entities. That many former slaves happened to be Christian (such as St Patrick) and preached manumission probably didn't hurt Christianity's popularity either. Good sources include Siedentorp's "Inventing the Individual" (London: Penguin 2014), Hollister, "Medieval History: a Short History," (Boston: McGraw Hill 2002)

The second is that Catholicism in particular had powerful state backers, or quasi-state backers that assisted in the propagation of that religion in new areas. While sometimes benign (Belgian religious hospitals in the Congo, for example), this was often not the case (the Templars in Lithuania, a great deal of what happened in South America). Readable sources include Holland's The Forge of Christendom (not scholarly but has a decent bibliography IIRC), the Jesuit Relations (for their treatment of how the Jesuits managed to use the French administration in New France to assist with evangelisation).

The third is that Catholicism was strongly related to the provision of either social services, such as education, and social advancement. Harold Berman's thesis, which traces the growth of the civilian court system in conjunction with ecclesiastical power, is an interesting read.

It's an interesting question, though very large. I'll go back and make some edits to provide more and better sources.

Follow on question: in the 19th century, the church began adapting their rites and missionary practices for local cultures. To what extent did this impact conversion rates?

Follow up question: To what extent did other European Christian religions successfully convert a population and was it any less successful than Catholicism?

Your question is very broad as conversion has happened in many different places, times and cultures.

But as you're asking for any reasons, I'll try to provide one. Please keep in mind that this is about a particular culture in particular time and place: Badeng Kenyah people in Borneo (Sarawak, Malaysia) after WWII.

My source is this interesting paper which deals with your question and covers conversion to Roman Catholicism and Protestantism: It Is Easy When You Are a Christian: Badeng Kenyah Conversion to Christianity (Tan Chee-Beng, 2016, Sun Yat-sen University, Guangzhou, China)

In this article, I explore how the Long Geng Badeng Kenyah community of Sarawak converted to Christianity even though there was no sustained missionary persuasion from the outside. Over a period of study, I eventually accept the simple emic explanation that “it is easy when you are a Christian” to be an important explanation. Central to this view is that Christianity provides an alternative religion that allows the people to avoid the need to observe the many troublesome taboos that hinder frequent traveling and engaging in various kinds of economic activities. The influence of relatives is an important factor, too, and as more people become Christians, the traditional Bungan followers lose the support to continue with the traditional religion and eventually almost all follow their relatives to adopt the new religion, which they find do not hinder practicing their culture other than replacing the traditional worship with the Christian way. The ethnographic study provides the opportunity to relate to recent scholarship on the anthropology of Christianity, and facilitates anthropological reflection on the study of cultural change, in particular, in relation to the work of Marshall Sahlins.

Before anything else I want to point out that living in jungle in Borneo is hard. Surviving is hard and prospering even harder. It all takes a lot of hard work and smarts, especially with the rather primitive technologies tribes had in those times - also please note I called technology primitive not people who were certainly not cavemen living in stone age (as British Rajahs used to say "they're not inferior, just different").

The first thing to note is that conversion was a gradual process in which Badeng chose to replace some old beliefs of adet puun with Christianity. In the process some initially chose Christianity which led to more people converting to it. These processes took mainly place after the WWII to about 1970s (but continued to '90s and out of this subs scope). In the 1950's also another religion was spreading, adet Bungan, which was a new streamlined, reformed version of adet puun with less rules and restrictions. For example, in adet Bungan some cumbersome things such as observing bird omens were dropped. Many Badeng did convert to that, and then over time to Christianity.

When I call things cumbersome I don't mean that as an insult on their old belief system. But it was restricive and even troublesome to the point of being counterproductive. Making a living in jungle is hard enough already without killing your valuable domesticated animals as sacrifices, without numerous taboos and without having additional rules and restrictions such as: when working in forest and hearing a kingfisher it is a bad omen and you have to stop what you're doing and go lie down for three days and nights. Or: if walking to work or traveling somewhere and a certain bird flies from left to right it is a bad omen and you have to turn back and try again the next day. Observing such omens does not tend do contribute to your prosperity but is rather counterproductive. It's living in jungle in the Hard Mode so to speak.

And that is what the people themselves say about it. They say that the old way, adet puun, was too restrictive. Converting to Christianity ment that they didn't need to observe the numerous rules and prohibitons of the old religion. Some scholars may see that as a mere post-hoc rationalization of their conversion. Yet that is not what the people themselves say. And I do think they're serious when they say "it is easy when you are a Christian".

The paper also brings up other reasons, but I promised to give one.

Also, if you're interested here's a book somewhat relevant to your question. It's about another tribe in Borneo: KELABITS' STORY THE GREAT TRANSITION, by Sagau Batu Bala. The author is a Kelabit and brings up similar issues with their old religion.

I interviewed many older Kelabits about their old cultures such as irau, jar coffins, traditional spirit worship, making kawang, head hunting etc. The problem of traditional spirit worship, the belief in ominous signs and taboos in their old culture threadened their survival. On seeing a snake or a baboon or a monkey or a civet or other such animal in a farm which was half way completed the farm had to be abandoned. If any of the same appeared to a newly married couple while on their way to their farm or they saw it in their farm they had to be separated and divorced. When a child was born during bad omens and taboo it had to be given away or left to death. If in the midst of building a longhouse they heard a barking deer barked on their way to build the house the building of the longhouse had to be discontinued. When ngae' bird flew from the right to the left or made a sound on the left side of the footpath of a person or a group of people which they use on a joyrney, they must not continue their journey. Should they want to continue on their journey they must consult the ngae' bird the next day and the day after until the ngae' bird flew from the left to the right or made a sound on the right of the footpath which they wanted to follow. These were some of the things the Kelabits must observe in their life as traditional spirit worshipers. It was destructive and difficult life. They wanted to get rid of it, but on their own they could not.