One powerful factor for rulers is that Christianity and the church's seal of approval solidified their basis for kingship and eased dealings with local Christian subjects and with other kingdoms. Formal conversion of the crown was generally preceded by conversion among part of the population as Christian missionaries journeyed through pagan lands, and contact with (and bringing of captives from) Christian territories was fairly commonplace, so the break wasn't wholly abrupt, while as a Christian monarch you now enjoyed the support of church and clergy so long as you didn't seriously misbehave.

Most pagans didn't quite believe their religion to be "true" the way Christianity purports itself to be true.

To be a member of a pagan religion, you just had to be the ethnicity of that religion and participate in it's ceremonies and rituals. Christianity, on the other hand, is partly a philosophy that was debated, attacked, and defended. You'd be hard pressed to find a Norse shaman who wanted to discuss Christianity, while on the other hand Christians were the ones who had very compelling arguments for their religion, or I guess the point is that they at least had arguments.

Are we talking about converting from pagan to catholic? The conversions were mostly top down with the king and court converting and putting a catholic layer over lingering paganism that lasted underground for generations afterwards. The biggest reason is the King went from being in charge because blood and force to anointed agent of God, making fighting the King the same as fighting god. Then you had the ease of dealing with few bishops rather than dozens of local priests in religious matters. The priests brought in bureaucracy as they were literate and many became clerks for the King allowing greater control and communications. laws were written down and taxes became more formalised and legal agreements such as treaties and land holdings stopped being based memory.

There's a gigantic organization. It has connections to natural resources, contacts with traders and political leaders, and has an armed force. There's an opportunity to get your family/clan/town/region access to those resources, people, and arms. That same opportunity is probably being offered to rivals.

Enthusiastic embrace is the most logical option in a lot of situations.

Women often played a large role in pagan kings' decision to convert.

• Clovis, King of the Franks was convinced to abandon paganism by his wife, Saint Clotilde of Burgundy
• Æthelberht of Kent was converted by his wife, the Frankish princess, Saint Bertha.
• István I of Hungary and his father both agreed to convert so that he could marry Gisela of Bavaria, though István appears to have been a more faithful Christian than his father was.
• Mieszko I of Poland agreed to convert so that he could marry Doubravka of Bohemia.
• Vladimir the Great had a Christian grandmother, Saint Olga of Kiev, and finally agreed to convert so he could marry the Byzantine princess, Anna Porphyrogennētē
• Hermenegild I of the Visigoths was convinced to abandon Arianism by his wife, Ingund of Austrasia. (Though Arianism was a form of Christianity, it still fits the pattern).
• Władysław II Jagiełło agreed to convert to Catholicism so that he could marry Jadwiga of Poland and become king of Poland jure uxoris.

Two books I read recently, The Realm of Saint Steven and East Central Europe in the Middle Ages pointed out that converting often opened the door to Christian marriage alliances and that the idea of one god and one church often fit better with kings' missions to somewhat centralize their authority that the multitude of gods of pagan faiths.

It's difficult to judge what any of them were thinking psychologically, as ancient and medieval chroniclers generally did not seek to uncover their subjects' inner lives and motivations, as modern writers so often do.