As an expert on both manga, who's winning in a fight: coco or ichi?
If you somehow engineered a death match?
Ichi kills Coco in seconds. its not close. Ichi exploded an advancing wall of death, he could easily murder Coco in cold blood. Coco doesn't really have a lot of offensive, attacking magic, unlike Lets Fight Things Ichi.
HOWEVER. Coco has no reason to want Ichi dead, and if Coco has no reason to want Ichi dead, then Ichi's got no reason to want Coco dead. Ichi has a very strict moral code with death for death, and Coco is never gonna trigger it. The battle is a moot point. Coco doesn't seek to kill! She repeatedly tries to find solutions where everyone is safe, so she wouldn't be seeking to kill Ichi. Ichi wouldn't be seeking to kill her. It's really difficult to get Ichi into fights where he's not trying to kill, or at least severely wound. Since ichi has access to healing magic and Coco doesn't, he'd also be at an advantage to just. Stab her badly, and she'd likely die too.
A non lethal fight is a bit more of a toss up depending on what the Goal is, like Coco's ingenuity is excellent, and her ability to combine magic and create new magic gives her more diverse options. It is kind of a skilled swordsman vers bomb situation though. Coco's magic is intricate and detailed, Ichi's is massive and explosive. Coco has a love for magic and learning which means any quiz or knowlege based battle would put her on top. She can also read, write, and use currency without any issue, and these are all things Ichi has struggled with.
A lot of Coco's power and ability comes from community, from the work and collaboration she can make with those around her. With the full power of the atelier, vs Ichi, in a battle to capture but not kill, I DO think their collective power could take Ichi down. However on a full Team Desscaras vs Aetlier showdown, I think Desscaras could take them all no qualms. Esp. Well we JUST got chp 61...
If they had significant prep time, Coco might be able to create a puzzle or trap to get Ichi, like if she was sent to assassinate him. Additionally, if she was able to get advice and help from the rest of her aetlier, I think she could get him. Now how long she'd be able to hold him? unsure.
Should the two of them be pitted against each other in a fight, I think they'd end up talking and find each other very very fascinating and interesting!!
To Coco, Ichi is another skilled magic user. Not only that, but in his world, the truth she had believed about how magic works really is true. He's the one exception. It's sort of scary, but her world is scary too, and at least there's potential. But he can do such amazing things with magic!! And his outfit is really pretty, and she'd be interested in the magical tailoring of it.
To Ichi, Coco is a lot like Kumugi! She's amazing, she can do all sorts of really amazing magic! She can make a little ball of light! And her magic she has to draw?!!? Ichi couldn't do that, he's so bad at studying. Coco's really amazing! And magic is amazing too!
Their shared love of magic would draw them together, and they'd have a wacky little friendship about it.