CONS: It's #38 in England and Wales and also very popular on Nameberry. Short, possible pronunciation issues (thought it'd only be ez-mee vs. ez-may), no real nicknames, if you did want one (though it seems silly to me when the name's only two syllables long in the first place!).
PROS: Lovely mellifluous French name, meaning "esteemed"/"beloved"; easy to pair with MNs; distinctive; easy to remember; will be currently unusual in many geographical areas, at least for now; feminine but not overly frilly, gentle, strong, and elegant; formal yet very easy to wear.