Barnes basically runs the platoon through sheer force of will. Technically Lt. Wolfe is in charge, but Barnes gives the orders. Although it is not clear, Barnes must be a veteran of several tours. He is a survivor (it is mentioned that he has been wounded seven times). This survivability has created an aura around him that gives him sway over some of the men. They follow him because he is a winner and realizes the rules of war are made to be broken. The unit members that disagree with his "my way or the highway" style are cowed by the force of his personality. Barnes taps into the more primitive natures of men under extreme stress and channels this.
Sgt. Elias is the conscience of the platoon. Like Barnes, he is obviously a veteran of several tours. His experience has taught him different than Barnes. He is empathetic toward the men. He wants them to survive, but with their humanity intact. Elias puts a lot of emphasis in teaching the new guys the tricks of surviving. He cares about the "cherries" when most of the other men do not want to bond with the new guys because they may not be around for very long.
The movie is set in 1967 which is about a year before the war began to turn, but far enough in for the nature of the war to be locked in. Barnes and Elias represent the two forks in the road that the soldiers faced. Barnes represents the attitude that although the war was not going well, more effort would result in the fore-ordained American victory. Since the war was different from previous American wars and thus frustrating, Barnes represents the school of thought that conventional rules should not apply. The end justifies the means.
Elias represents the belief that the war is probably unwinnable and to win by losing your humanity and core calues is not acceptable. He mentions that America was due to get its ass kicked. He is not a pacifist and is, in fact, a very good warrior. But he is not willing to break the established rules of warfare just to "win".
The crucial scene depicting these differences is the village scene. If you watch carefully, Barnes is right. The villagers are obviously aiding the enemy. Forcing the village elder to talk will aid the war effort and possibly save American lives. Barnes obviously goes too far, but instead of shooting the wife, if he had put a gun to her head, would that have been justified? Suppose it was a terrorist situation today. On the other hand, Elias takes the approach that there are rules that can not be broken no matter what.