I think
Emilie looks really neat. For some reason it seems more feminine than
Emily, although I would never consider
Emily to be unfeminine! However,
Emily is SO popular that I think it would be a mistake to use a variant spelling. I certainly wouldn't.
I would use
Claire instead of
Clare because
Clare isn't that common and
Claire isn't that unusual.
Elizabeth and
Elisabeth are also both common, so both useable. I think the problem with Emily/Emilie is that
Emily is REALLY popular and
Emilie is practically unheard of, so the difference is much more obvious.