I like Emilie just as much as Emily. They're a little like "country mouse, city mouse" in my mind. Emilie has an old-fashioned prairie girl feel, while Emily feels a little more "citified"--more current, a little sharper.
I would use a spelling variant if I wanted to. My own name (Alison) has never been the most popular spelling in the US. When I was a kid, it bothered me some to look through racks of mugs or keychains and only find "Allison," but to say I got over that is an understatement. I just want the spelling variant to be well established. I'd use Gillian instead of the more popular Jillian, for example, but I'd never consider Gillyan.
Violet Emilie is adorable.