I won't speak for pagans across the board, though I believe they may follow the same general pattern. Instead, I'll look at the Vikings. There are a few reasons for the conversion.

The first and probably simplest explanation is that the Norsemen were remarkably good at moving into a region then assimilating into the local population. This may be a similar case to what happened with other pagans that adopted Christianity rather than be eradicated. They may have just been susceptible to new ideas. The Norse spread from the North Atlantic to Byzantium, but they had a fairly predictable pattern. They often get portrayed as brutal barbarians that just took what they wanted in raids. In actuality, they would raid an area, start leaving people in the area for easier raiding later on, begin establishing trade routes, begin establishing settlements, then assimilate into the native people to a point that you could barely recognize them as "Viking." And they'd do all of this in the course of only a few hundred years, repeatedly. It happened in England, Ireland, Scotland, France, Italy, Byzantium, and Russia. The North Atlantic saw smaller native populations that they often did not get along with, so that is different. Sorry that this went on for a bit of an off topic discussion, but pretty much they accepted Christianity because of their openness to other culture's customs after settlement.

Another explanation for their acceptance of Christianity comes from the attractiveness of the religion. First, the Northmen loved raiding monasteries. They were full of gold and undefended, so they began attributing that gold with the wealth that could come from Christianity.

Furthermore, Christian nations offered attractive benefits: strategic alliances, trade partners, technology, materials, and writing (which is quite good to have for a people that make a living through trading). These benefits would often not be shared with pagans until they had converted. Conversion, itself, was also often rewarded. I can't remember the exact story, but it is in one of the PowerPoints I use to teach. One Dane had reportedly "converted" 30-40 times, because each time he was given a pure white garment to keep. In another instance, Louis the Pious was offering a mass conversion of Danish pagans. They actually ran out of those white undergarments, and many men left in disappointment without going through it. There were legitimate benefits to converting

Finally, Christianity is an extremely useful tool in asserting power over a population. A fairly standard doctrine keeps everyone on the same page. u/itsallfolklore and I had a nice conversation about this kind of idea in a separate thread. Before Christianity, the pagan belief system was varied and constantly changing depending on who you asked. After Christianity, everyone has one core belief system that stays relatively the same throughout. There are definite variations, but it becomes much easier to unite people under one belief system with one main god. On top of that, the kings could assert their authority directly from God himself through the "divine right of kings."

Christianity was an extremely attractive option for the leaders of the Norse. And in the end, the leaders were what really mattered in the conversion of the people. At the end of the day, the people still held on to many of their traditions and even some of their gods; but Christianity would gradually take over.

Conversion often had little to do with the religion itself and was done for the benefits. It would gradually become more and more important as a religious system over time; but often they just wanted something out of it, whether that be power or material goods or whatever it may be.

Great answer by /u/FlokiTrainer. A few additional thoughts:

Some of the problem with modern perceptions of the excellent question you ask is in the word 'religion'. One could argue that what Christianity represented and what it confronted in places where it converted people in its first millennium were very different. One could argue that many pre-conversion societies did not really have religions in the sense of what Christianity delivered. They had belief systems and/or they had civic practices, but what Christianity introduced was something of a new kind of cultural element: a strict system of belief and practice with a hierarchy or priests and most importantly - a Book!!! Most converted societies that Christianity encountered simply didn't have this sort of thing, particularly after the 4th-century conversion of the Roman empire.

Consider the situation today if someone were to accept conversion and baptism. The priest would not even ask that person to give up elements of his/her belief system. That person might believe in ghosts, bigfoot, and extraterrestrials visiting us. And who knows what that person might belief about the Kennedy assassination. The priest wouldn't ask for any of these beliefs to be replaced.

While there was some replacement of indigenous beliefs, much of these beliefs were perpetuated (consider the Northern European beliefs in fairies, giants, and a wide variety of other things, all of which survived - if mutated by - the conversion process).

There was a pre-conversion belief system that was confronted by an organized, steamrolling religion. The belief system yielded, but it did not entirely disappear when confronted by this new type of cultural strategy for the new world that was emerging in the first millennium CE.