I think Emilia's favorite genres would be romance, fantasy and maybe drama, though she would most likely be quite picky there.
Romance is an easy pick, as it is more or less canon, that would she come to this world, one of the things she'd enjoy most would be Shoujo manga. As such it isn't too far of a stretch to infer her enjoying the romance genre in terms of movies as well.
As for fantasy, those movies might be quite confusing to her at first, given that magic and a whole variety of mystical creatures do exist in her world anyway. So she might get a little confused if magic systems and such in the movies deviate heavily from what she is used to. I still think there would be quite a few movies in the genre appealing to her, and the deep narrative some good fantasy movies come with would be quite enjoyable for her as well.
I am a little unsure about drama, but would still say that there would be some things in that genre that we would enjoy watching together, as long as it doesn't hit too hard.
As for the genres she would like the least, I'd go with horror, action, and crime movies.