He doesn't like to lose control. It's a trait he gets from his father, or at least from unconsciously trying to be like his perception of his father. Even after years of cursing the name of the man who failed to raise him and pushed his brother to his death, he can't help wanting to be more like his childhood hero.
So he doesn't let his anger show (except to his father and Kara and occasionally, embarrassingly, President Roslin...and, well, the deck crew doesn't really count, do they?), and he tries to appear confident and self-assured no matter what this new life throws at him.
But he's not his father, whether he wants to be or not. He is young and passionate, sure of his beliefs but unsure of himself. He cares, perhaps too much, about people, and about right and wrong and justice and all the ideals that were left behind when human existence became about nothing more than survival. He hasn't yet learned to destroy and forget, to shoot now and not ask questions later, but he will have to or this interminable war will break him.
He's always been a quick study, and already he's learning to do what's necessary. The Lee Adama who flew in Galactica's decomissioning ceremony would not have been able to destroy a ship that might be full of innocent civilians. He would not have effectively played the crazed interrogator to an assassin who was only a pawn in a greater political game.
He wouldn't have had to, because for that old, forgotten Lee, the Cylons were little more than a moral lesson, a warning against playing god or going too far in the quest to make life easier. For Captain Apollo, CAG of the last remaining battlestar, they are the enemy who destroyed the Twelve Colonies and nearly everyone he ever knew, and to save humanity from them he is willing to set aside some of his prized morals for the time being. For all his desire to control himself and his life, he really has no choice.