As we see the events that bring about the downfall of Talbot, it's hard not to take sides. York seems genuinely distraught that he can't do his duty as leader of the English troops and help Talbot; he has no troops to send. He curses Somerset for not having provided the cavalry that he promised, but then he ceases cursing Somerset and curses an unspecified "cause" of his inability to help Talbot. Is York, thus, no longer blaming everything blindly on Somerset but attributing it to some impersonal forces? Somerset, however, is not so genial. He accuses York of having sent Talbot to his death so he might take over the honor of the military leader. And he denies that York had asked him to send his cavalry, adding that he wouldn't have wanted to help York anyway. He shows little remorse that the death of Talbot and the fall of France may stem directly from his selfishly motivated delaying. He is merely concerned with blocking all help to York.
These scenes portray the struggle between York and Somerset in a different light. Whereas earlier both men appeared equally foolish and petty, York now seems the better man. He wants to help Talbot and is upset that he can't, while Somerset remains callous and thinks Talbot's death was merely engineered by his enemy York. The audience sympathizes with the honorable Talbot; now that York tries desperately to save him, we begin to side with him as well.
Did Shakespeare intend to make York look better than Somerset in order to compliment the descendants of York in his own time? Perhaps. But regardless of whether the playwright had ulterior motives, the new light he sheds on the lords' dispute also helps to develop and differentiate these men as dramatic characters.