Ok so I'm fairly certain Boyfriend takes battle IQ here by his fights with Murder!sans and Pico.
From what I know about Dustin'... not really? Muder!sans is 90% singing with like a single Gaster Blaster at the start and a very simplified danmaku sequence in the Hotland song. Boyfriend did manage to beat Sans, but the profile indicates that it was done by becoming so much stronger with determination that he could just blitz Sans before he could do anything like... dodging his attacks repeatedly in the song prior to the blitz, meaning Boyfriend doesn't really get skill from that.
As for Pico, his fight with the army is entirely off-screen and what we do know is that Pico was obsesssed with EXP and is so strong that not even Boyfriend could beat him. It is entirely possible that Pico was just grinding EXP like a typical RPG character on weaker enemies and engaged with the army after he became too strong for them to be able to fight back anymore. So it could be a decent skill feat, but there's not enough information to reasonable conclude that.
As for Charlotte, she was actually able to make short-work of Frisk that has a pretty similar moveset to Boyfriend (though that's because Boyfriend is taking the role of Frisk in the mod), and Frisk able to take out a reasonable chunk out of Nightmare Springtrap's army even while heavily injured so and evade attacks from Nightmare Springtrap himself without taking any hits so... yeah, both don't really have a lot of skill feats but Charlotte's are quantifiably better in my opinion.
He can also probably range spam and his social influencing + broadway should be useful in letting him dictate how the battle goes
Broadway Force's scan is missing (thanks imgur, very cool!), but from what I can tell it shouldn't really stop Charlotte that much. The justification only implies that it compels the characters to sing, which doesn't necessarily mean that they'll
only sing and nothing else, something which is supported by the mod where there are like MULTIPLE instances where characters attacking and inflicting damage on each other during songs.
Oh speaking of the other points, Charlotte's smelting has far more range and AOE than anything Boyfriend has shown and it would
immediately throw the battle into her favor with what it does to the environment once performed (It's also Charlotte's starting move) as she'll be abe to maneuver through the lava while Boyfriend... cannot.
As for Social Influencing... Flowey's profile says that he can easily frightened, so Boyfriend can't have Fear SI if that's the case. Even then, Murder!sans was completely unaffected by BF's SI and Charlotte can easily learn anything about Boyfriend
including his past and future just by viewing his face if he does that so...
If you ask me,
my vote is on Charlotte as nothing prevents her from just smelting the battlefield in lava and then destroying whatever platform Boyfriend was lucky to land on and
she can easily do the same trick she did against Frisk with Boyfriend if he attempts to fight back at range.
