Even though Megumi lost her match against Momo, on some levels it still really counts as a victory. Not only did Anne recognize her skill and Momo finally drop the patronizing nickname (thus indicating that she recognizes Megumi's talent), but when Megumi breaks down at the end, it isn't because she thinks she screwed up or somehow wasn't worthy. While it could just be Soma's take on things, I do think he's right when he says that she's crying from frustration. Megumi outdid herself, was confident in her recipe despite the tension and the taunting, and she still only got one of the three judges on her side. But mostly she knows that she didn't do anything technically wrong, and for someone as timid and anxious as she is, that's a major win. She's now seeing herself as part of the group, and worth being part of the group, and even though she didn't beat Momo, she triumphed over her insecurities. That's going to mean a lot going forward, and maybe she'll even bring herself to take Shinomiya up on his offer to help her get stronger.
After her card went to Central it's still cathartic to see Takumi wipe the floor with Eizan, though. While no one in Central is perhaps winning prizes for charm (although I suppose Tsukasa comes closest; poor guy really just seems to want to be left alone to cook), Eizan is arguably the worst. Sure Rindo is competitive to a fault and Momo's a twit, but Eizan enjoys being the biggest jerk he possibly can be. He sees it as fair play, because he's in it to win it, and it's not his fault if no one else brings the same passion (i.e. lack of scruples) to the table.
This, however, is precisely what's behind his quashing at Takumi's hands. Eizan assumes Takumi to already be broken after the Fall Classic, when he lost hugely to Mimasaka, and he can't imagine that the first year would be able to bounce back from that. In Eizan's world, winning is everything and anyone who suffers a double defeat (his cooking and his knife) the way Takumi did has no right to even keep playing, because obviously he doesn't have the wits to do so. Therefore, Eizan is far too secure in his own superiority and underhanded – although not technically illegal – tactics, and that's what leaves him open to defeat. He doesn't realize that someone could use the exact same thought processes and set of predictive skills against him, possibly because he's so used to being the only person who would go so far as to actively sabotage the taste buds of the judges in a major competition. So when Takumi reveals at the end of the episode that he was counting on Eizan attempting that very thing, Eizan is blindsided, especially since Takumi turns out to better at it than Eizan himself.
Tsukasa may technically be the guy with the “White Knight” nickname, but a lot of this particular card plays out like a battle between the hero and the evil overlord. While Eizan's faces help drive that comparison (although one shot looks more like a scene from Cells at Work! than anything), it's more in the way that Takumi doesn't allow the villain's monologuing to get under his skin and then quietly exploits the one unlocked grate in his castle, so to speak. Not that Takumi is above boasting of how he pulled it off, but he waits until after the battle is over to do so; Eizan, in true bad guy style, pretty much spends time explaining to the hero how he's defeated him instead of just taking him out. Classic villain mistake there, guy.
In terms of character development for Takumi, this whole thing shows that he's learned to master his own temper. He's still burning with the need to prove his worth, but he's not rushing into things any more – his confidence has been tempered by his losses and the things he's learned. While he's also certainly on the path to joining Mimasaka in Creeper Land, he's made a lot of progress and become more secure in who he is as a chef. And as with Megumi, that's the real victory for his battle.
Food Wars! Shokugeki no Soma: The Fourth Plate is currently streaming on Crunchyroll.