I'm not sure if this is too vague a question. I suppose it might have varied from battle to battle, century to century. But still I don't quite understand how two armies would come together and in some instances one army win so decisively . eg The battle of Agincourt or Cannae (tactics aside how were the troops in the smaller armies not be overwhelmed?) Cheers.
In ancient times actual losses are estimated to be only about 10% - 15% of casualties. (Harry Sidebottom, Ancient Warfare, Oxford/New York 2004) Usually, battles were decided by making the enemy line break and rout. Think of being in a dense formation were you couldn't actually see the battle due to other lines of soldiers being before you. If you think the lines before you are breaking, you might just choose to turn and run instead. And as a front line soldier, you wouldn't keep fighting if your comrades behind you choose to leave the battlefield. The Greek and Roman armies were so effective because the Hoplites or Legionaries respectively were disciplined enough not to flee at the first sign of weekness in the formation.
In terms of battles being a meat grinder, it is still debated whether in Hoplite battles combatants actually took a break. (Harry Sidebottom, Ancient Warfare, Oxford/New York 2004). If I'm not mistaken, the Romans rotated front lines to keep soldiers fresh. Although there are some mistakes as well, this scene from the popular series Rome might give you a rough idea: http://www.youtube.com/watch?v=gbSa9ZvSMaQ Unfortunately I don't have primary sources on this and would be happy as well if someone could tell me whether there actually are.
The decisive battles of Agincourt and Cannae were somewhat special: At Cannae, the Romans were enclosed and weren't able to flee, which made it so devastating. At Agincourt, a lot of knights were actually captured at first rather than killed. In Medieval times it was more common to capture a noble and demand ransom instead of just killing them for various reasons (financial ones, or not unnecessarily obliterating your (noble) class by killing each other). Only when French cavalry attacked the English camp, the captured French nobles were killed.