Yeah, Eileen doesn't overtly dislike Bigby. Her willingness to kill someone and how much she likes them have no correlation at all - she just doesn't trust the self-control of a wolf-monster, is all. Call her old-fashioned, if that's what it makes her. The fact that Bigby also kills other monsters definitely endears her to the sheriff, while simultaneously making her more dangerous in Eileen's eyes.


Of course, it's becoming increasingly obvious that Eileen couldn't actually win a fight with Wolf!Bigby so there's that.