I don't know anything about Yuuri, so I'll have to go by her page. Both seem to have pretty similar abilities, with Kumoi having a good edge in the illusion front (though Misaki is no stranger to making complex illusions as seen in Misaki SS, hers doesn't have that "you die on it, you die for real" part). If esper powers are equalized both should be able to resist the other's power, so a mind clash would mean a battle to break the mental defenses of the other. Misaki was good enough to block
Kihara Gensei when he had access to Exterior for as long as she was conscious, so unless Yuuri has some pretty impressive mind feats I don't think she's beating Misaki. However, the same can be said for Misaki, as
Mitsuari Ayu's Level 3 Mind Stinger was enough to shield her from Misaki's power. I don't think the mind battle would be quickly won either way unless Misaki has access to Exterior.
What I think decides this battle are the bystanders, and that's where Misaki seems to have a slight edge. With her better reactions and her smarts, she'd likely make the bystanders attack Yuuri as she fights her mentally pretty soon into the fight, as she's a pretty paranoid person that would take no chances in a confrontation like this one. Misaki can perfectly control around 10 people, and if they are simple commands such as "stop moving" or "attack that person", she should easily be capable of setting a crowd of dozens on Yuuri. That would be dangerous in London, even more in AC given the espers, Anti-Skill and Skill-Out who could be around for Misaki to use. Misaki's better range means that once this situation starts she can start mentally attacking Yuuri from outside her range as she looks for more people to "recruit".
My vote goes to Misaki in both rounds. I think Yuuri's best shot would be in the second roun by copying a good esper power that would allow her to fight all the people that would attack her at once, but that would be up to luck.