I know that the majority of battles were not fights to the death. Often one side would rout and flee after a certain point. But, hypothetically, if me and my mates know we're in a hopeless situation and we have enough control over ourselves to not run immediately, would we fair better if we dropped our weapons and surrendered? How likely would it be for us to receive quarter, and if we did, what would probably happen to us next? Should I have just tried to run instead?
As a side question, how would this change if I was a knight or nobleman?
In many ways, warfare in Catholic countries in the 14th, 15th, and 16th century was a speculative business venture. The soldiers provided capital (their horses and harness) and labour to do something risky with a chance of a high payoff. One of the these payoffs came if you captured someone important and held him or her for ransom. Ransom was basically a private relationship between captor and captive. It is only around the 18th century that some states claim responsibility for protecting all of their soldiers if they are captured. A lord might pay ransom for a follower, as when Edward III paid Geoffrey Chaucer's ransom, but that was not guaranteed.
So if you were not obviously rich, your prospects if you surrendered to another Catholic were uncertain. Since Catholics could no longer enslave Catholics, a soldier was only worth what his family could pay for him (not what a slave-trader would pay for his labour). And taking a prisoner meant you were not looking for another prisoner or looting the baggage train or otherwise getting rich. Descriptions of battles in the high and late middle ages are littered with descriptions of the infantry on the losing side being slaughtered while the gentlemen were taken prisoner. One reason why it was a powerful gesture for the gentlemen to fight on foot in humble clothes was that they could not mount and ride away, and could not rely on their dress to show that they were worth ransoming. William Patten's description of the Battle of Pinkie in 1547 contains some beautiful complaints that since the Scots all dressed alike, the English victors accidentally killed some of the lords and spared some of the peasants, which was the opposite of what they intended.
The private nature of ransom created other problems. Fourteenth-century knight Geoffrey de Charny asked his peers what to do if soldier A took a prisoner, and soldier B came up and said that either A would share or B would kill the prisoner. If the prisoner was important enough, say King Jean of France in 1356, their capture had political implications and they would end up in the hands of someone of appropriately high station. There were many robber knights who would capture travellers and torture them so that their family would pay as much as possible as quickly as possible. And taking prisoners (and looking for the richest possible prisoners) could distract soldiers from their work, leading to the infamous massacre of the prisoners at Agincourt when King Henry was worried the French would launch another attack. There were also political aspects. In a civil war, the winning side might want to wipe out the leaders of the losing faction, and not care about the ordinary soldiers. Ordinary soldiers often tried to surrender to a knight or lord on the grounds that the knight or lord would be ashamed to kill or abuse them like a common thug, but knightly armies could be vicious to commoners who challenged their authority. So sometimes, especially earlier in the middle ages, the knights brutally slaughtered the enemy foot. If "the value of a thing is what that thing will bring," the life of a cobbler or a blacksmith's son was just not worth much.
If you were losing a battle and could not get away, a common strategy was to get somewhere that you could not be casually killed and slow things down. We often hear about this in sieges, where some of the defenders occupy a tower or other building as the place is falling and negotiate their surrender. When nobody's blood was hot and everyone had time to think, surrendering was safer.
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