I can't find the video online, but the special Going Medieval, presented by Mike Loades, covers aspects of this. He begins discussing singles combat at 5:20, I typed out the transcript below:

Loades: What would happen in a battle is the crush of men from either side squeezes you in… They’re getting closer and closer, and eventually they’re in a tight melee. Finally, they have no choice but to fall to grips and grapples. Wrestling techniques were of particular use when knights came upon other knights on the battlefield. They had their own code of honor: Chivalry. And my sparring partner, Dr. Tobias Capwell (Curator at The Wallace Collection, a national museum in London), is an expert in the rules.

Dr. Capwell: Knights are fighting other knights, other equals of the same social class. And within the brotherhood of chivalry, you don’t necessarily want to have to kill your social equals all the time. You have the process of ransoming; you can force them to yield to you, they become your prisoner, and then you can sell them back to their family for an extraordinary profit. But they’re not going to yield easily.

Loades: You’ve got to defeat them, but not kill them.

They then demonstrate how one knight can put the other in an arm-breaking position (screenshot). Dr Capwell (top) can make it worse and worse until Loades (bottom) yields.

Loades: I yield, and then I give you my word: ‘I yield, I am now your prisoner, you can let me up’. Chivalry works with people of the same class. Of course, if he does not perceive I am of his same social class, then Chivalry doesn’t work and he drops me to the dirt.

So, it all comes down to whether or not the "losing" knight or nobility is willing to give himself up, and if the aggressor see's this person as having the equal social standing to be considered trustworthy. They mention the money that could be made by ransoming the losing party, so it certainly gives the impression that it would be far better to take him prisoner. If a knight or noble would submit to a peasant, even in the face of certain death, is a different question. And unfortunately, it's an answer that I do not know.

It's an interesting question and one I would like to see answered by better minds than my own since, for the most part, I have been unable to locate any reliable form of record either way.

(apologies in advance btw, a half assed browser hijack just killed my better post)

Where as in field rewards for gallantry etc were common I cannot find many 'rewards or punishments' expliticly stated for killing a noble during open conflict or even under tournament conditions. (Gabriel the count of Montgomery accidentally killed Henry II of France in 1559 by a lance wound to the face, Gabriel requested execution for his act, but the dying king forbade it ~ The Queen of Pubes bore a grudge though so don't discount the people, social norm and exceptions abound).

Within The Law of War and Peace by Grotius 1625 there is no mention of punishment for killing under war conditions but only percieved legal or illegal killing. (poison is illegal for example)

During the Hundred Years War ransom taking was the go to get rich quick method even going so far as to be formalised and taxable. Prisoners of War in the Hundred Years War: Ransom Culture in the Late Middle Ages. Actually Remy Ambuhl has made a fascinating study of it.

For other information i would suggest Juliet Barker. (Conquest & Agincourt)