I think Broil goes back to stuff like Leeches; SCH is kind of a "Doctrine of Humors" era medic. I also really like Broil IV's animation (more than its predecessors) since it makes me think of plasma weaponry from Halo or something:

Pistol: https://youtu.be/fLEVKa465cc?t=63
Rifle: https://www.youtube.com/watch?v=_wp4RXWo3C4
(Can't find video of it, but the red plasma turrets also sound like that, especially hearing the plasma hit rocks and stuff)

And, probably because of this association, I like Broil IV a lot since "plasma weaponry" sounds like something fitting of a military scholar-mage. I also like the sigils and glyphs. Ever since "Holy Light" in Chrono Cross when I played it like 20 years ago, I've loved spells with word/symbol components visually part of the spellcast. Both Broil IV (and Broil III) and Art of War II have these, and I love it. I hope they get more over time.

I think one of the things I like about SCH is how NON-flashy it is. It feels somehow more grounded. I also like when my shots streak at the enemy, so I like Broil (other than Broil 1 itself) far better than, say, Fall Malific (which I can't even see most of the time) or Glare III (since it's also easy to not see much of it depending on what else is happening on screen).

But this is absolutely a personal taste thing.