Since the story in Rakudai is focused so much on the Seven Stars Sword Festival, the chances of it going full Mahou Sensou is low. Not sure about Asterisk yet. I'm still reading into it, and the story right implies that the volume is all about special people with abilities beating the shit out of other special people with abilities.
Oh, and there's also a tournament in Asterisk, but it involves six schools based on former nations and thus, more global in a sense.
Rakudai Kishi somewhat reminds me of Unbreakable Machine Doll, primarily because it involves competitors in a large-scale battle interacting with each other, and because of a greater focus on building relationships as well as making sure that the tournament also proceeds simultaneously.
As for Asterisk, I don't know. The world is completely different (especially politically) after Earth is bombarded by meteors, and the biggest sporting event is sponsored by a corporation with a world-wide influence. It feels like The Hunger Games, right? I'd say the comparison is sound enough.
Rakudai Kishi feels rather low in the chuunibyou department compared to Asterisk.
I'm only picking up Asterisk and Rakudai Kishi, so you have to ask someone else about Anti-Magic.
Asterisk, on the other hand, is still unknown to me because I haven't read the source.
Spoiler for plot details up to Vol. 1:
Rakudai Kishi focuses on Ikki Kurogane, a descendant from a prestigious clan of Blazers, who now studies in one of seven Blazer-affiliated schools in Japan, Hagun Academy, as a repeater.
[Blazers are gifted people who has the ability to materialize weapons and utilize magic. Under a worldwide set of regulations for Blazers, Blazers are required to study to be "professional" Blazers called Mage-Knights, who are allowed to return to society to assume regular occupations or to fight rogue Blazers in anti-crime and anti-terrorism units.]
Despite his background, Ikki is unable to graduate because the strong influence of the Kurogane family manipulates the system used in the school so that he doesn't acquire his license as a legitimate Mage-Knight, something that stemmed from Ikki's "poor" Blazer abilities (and you can say the family's immense ego). Of course, the rest of the school don't know this, so he is instead called the "Worst One" for being the last in the scholastic rankings.
He meets one of the strongest Mage-Knights in Hagun Academy, Stella Vermillion, in an embarrassing encounter, and the foreigner princess challenges him to a clean duel, but eventually gets defeated when Ikki shows his ability to replicate the swordsmanship of an enemy to counter her attacks. Because she lost, the current headmaster and a radical leader who opposes the injustices committed to Ikki, Kurono Shinguuji, permits the two to share the same room. Kurono also reveals that she has made a deal with Ikki, allowing him to graduate IF he wins the Seven Stars Sword Festival, a Mage-Knight tournament that pits the strongest among the seven Mage-Knight academies in Japan.
Stella eventually learns of Ikki's struggles as a boy betrayed by his own family, and she also exposes her past as a girl who simply wants someone to properly acknowledge her true strength. Their relationship blossoms since that moment of understanding.
Most of the story after Volume 1 is spent on the Seven Stars Sword Festival-related events, although there are also some background about Rebellion, an active Blazer-supremacist group. Romance-wise, it always emphasizes on the Ikki-Stella couple more than all else.