I thought the reason that The Lich King was caged in the Frozen Throne was because even Kil'Jaeden feared the monster he had just created, and didn't want him to get out of control.
Then, when Ner'Zhul merged with Arthas, the Lich King became vastly more powerful than before. And then again, Frostmourn takes souls and those souls feed the Lich King's power. There is no telling how powerful the Lich King was before his defeat. I do know that he was able to snuff the lifes out of Azeroth's greatest heroes after playing with them for ten minutes. Even Deathwing couldn't do that.
As for The Lich King vs Deathwing. The Lich King plays with his soon to be new toys for 10 minutes before killing you, and in reality the Light is the only thing that defeats the Lich King. Deathwing is actually held at bay by the heroes. Though the heroes couldn't have defeated Deathwing without the Dragonsoul, they were still able to delay his casting of the second Cataclysm.
If The Lich King had wanted to kill you, and Tirion, he could and would have without even breaking a sweat. His own arrogance and the Light are what brought him down.
I say this because I think that The Lich King is by far the most powerful being that the heroes have fought thus far. The Old God's were slain with some minor health, Illidan was slain with the help of only one other mortal. Deathwing was held back long enough for Thrall to do his Goku impersonation to kill him. The Lich King? It took the full force of the Light to defeat him, and that was only enough to shatter Frostmourne and dispell a lot of the Lich King's power.