I'm certainly not an expert on Norse mythology/religion or ancient Christianity, for that matter; however, I'll share what I believe to be the characteristic of each is which is most exemplified in the epic poem Beowulf.
The Norse pagan beliefs of the day centered around the concept of fate. They believed what did or did not happen was more a matter of fate or chance (accident) than anything humans did or planned. This belief made for fierce warriors and passive kings in Beowulf, it seems to me. Beowulf is a rather reckless fighter, taking more risks than he probably should. He does so because he believes he will live or die as fate will have it. Knowing that, he is more apt to be less prudent when fighting (as in fighting Grendel without any weapons). This concept of fate is prevalent throughout the poem, seen in such lines as:
But death is not easily escaped from by anyone; all of us with souls, earth-dwellers and children of men, must make our way to a destination already ordained.
In contrast, Beowulf is also a Christian text which reflects Christian beliefs and practices such as prayer and God's protection for those who pray. Because this is an ancient poem, it wasn't written down for literally centuries. when it was, it was the Catholic monks who did so, routinely inserting the contemporary doctrines of the church into the written text. Lines such as the following were not reflective of the more pagan beliefs of the day:
And the Geat [Beowulf] placed complete trust in his strength of limb and the Lord's favour.
As an epic hero, Beowulf does exemplify some characteristics of the Christian tradition, as well. He enters the battle with Grendel unselfishly, recognizing another's need and meeting it because he can. He fights for his own honor, but he is also quick to give honor to his King. He is loyal and true to that King until he dies.
Perhaps this will give you a start, at least, as you think about more comparisons on your own.