I think I always prefer
Katherine. I don't mind alternate spellings - it just disappoints me a little because the change to the spelling fails to make the name more appealing or striking to me, maybe because the name has so many spellings and forms.
I guess if I ignore which spelling is easier, and it's purely about aesthetics (and I'm sure you mean that it is!) I would wish to avoid the paired Ys of
Emily Katheryn. So,
Emily Katherine would be my favorite, but
Emilie Katheryn is better than
Emily Katheryn.
- mirfak