Joan's tactics against Burgundy in these scenes do make a strong case against the old style of chivalrous warfare. Why did Burgundy come so trustingly to speak with his enemy? Presumably he, being an honorable man, thought the French would act honorably, too--that there was no harm in having a reasonable conversation with his enemy, since they weren't actually fighting at the time. But the dangers in such a move seem obvious.
In Joan's modern version of battle, the war is always going on, even when it's less a pitched battle than a war of wits. And in this case she wins, convincing Burgundy in a few paragraphs to stop fighting against his countrymen (Burgundy was a French lord who sided with the English)) and to join the French. And he is unable to resist. Was her rhetoric so convincing or did she trick him in some way with her magical powers? Either way, the upright and noble Talbot would never have suspected anyone of such a sneaky tactic as luring a warrior to change sides; thus, he will fall to Joan.
The argument between Basset and Vernon shows that the struggle between followers of the white rose and the red rose has crossed the Channel, and it will threaten the coming battle. Vernon and Basset know they are forbidden to fight with each other, but their mutual hate is so intense that they will find other ways to harm each other. The battlefield will probably end up being the site of their argument's climax; who can stop them from fighting each other in the middle of a bloody struggle between the British and the French? Hence, the British forces will be divided against each other, weaker than ever against the French.