I went with Jaime. Getting inside of his head in his chapters is fascinating.
Most Improved? Probably Robb. In life, he was too much of a walking cliche for my taste. He was a rich, powerful, noble, heroic, teenage king with a superwolf... If I've read one fantasy story like that, I've read a hundred. In death, he's much more interesting... he's a martyr... he cries out for justice... In death, Robb has become a cause... I'd love to see a cult arise from this... the Cult of the Young Wolf.
Or mayhaps Joffrey is the most improved. In life, he was annoying. His death pleased me greatly.
But seriously... if most improved means maturity, then I'd say in order they are Arya, Dany, Jon, Jaime, and Sansa.
If most improved means becoming a fascinating character, then I'd say Jaime and Tyrion.
Jon.
He held The Wall against the Wildings while being a half crippled teenager.
He killed the Halfhand on order, has protected Mormont, bantered well with Stannis, made the decision to send Sam off with Mance's baby, and has become the head of the Nights Watch in place of the Old Bear. He was handpicked by Noye, and told Slynt that he, "doesn't know what your head is full of."
He has become a youthfull embodiment of: Night gathers, and now my watch begins. It shall not end until my death. I shall take no wife, hold no lands, father no children. I shall wear no crowns and win no glory. I shall live and die at my post. I am the sword in the darkness. I am the watcher on the walls. I am the fire that burns against the cold, the light that brings the dawn, the horn that wakes the sleepers, the shield that guards the realms of men. I pledge my life and honor to the Night's Watch, for this night and all the nights to come.
I won't argue with the picks of Danny or Jaime, but for me it's Jon.