I will use Finland as a example for this.

When in the 1150's the population of Sweden increased rapidly, this led to a lot of sons left with no inheritance. At this time there was less "good" land in sweden due to the weight of the ice from the last ice age had pressed the earth down so the land mass of scandinavia was less than today.

When the Swedes who emmigrated to finland in search for "good" land arrived there was no settled land in the finnish coast, due to novgorodian raiders and so on. Well the finns and the Swedes had most likely had great relations dating back to the viking age.

Back to the main question, the reason why the finns in this case converted was to become a part of the European system, as a Christian you could be lucky to have to chanse to learn how to write or read, you could go to university. The Viking kings knew about this and converting wasn't easy but it was better than the alternative to become a target of a holy war.

Many of the eastern pagans, especially the baltics who was under constant attack by the german knights (Teutonic Order) had two choices, Convert or die.

Christian nations who had an interest in the pagan terretory often followed the same pattern, first they sent in the chrisian people, after them came the curch.

One could argue that paganism at that time was like using a typewriter today, a little out of date.

Then you also have to take in mind that this was also in a time which is known as the dark age. In all of the land from the old western roman empire was left in dispare. There was no strong economies, no stong govenment in the entire region. Therefore the church became all of that. it's because of the chaos that followed the dismantle of the western roman empire that gave the curch such a dominant position.

Sources:

The colonization of western uusimaa in the middle ages, 2011.

Tuomas Heikkilä "st henrikslegenden" 2009

Mikko Heikkilä "om Finlands väsliga och kyrkliga införlivande med Sverige " 2013

PS. Even if my example with finland isn't exactly early middle ages the benefits for converting was almost always the same.