If you’re asking which one I would prefer,
Jasmine hands down. It’s pretty, the name of a lovely flower, appealing spelling and sound, and you have the nickname Jazzy, which I find real cute. I’m not crazy about
Jazmin as a spelling or anything else but it’s okay.
As to
Emerald, ironically enough the only
Emerald I ever knew is a boy. I know gemstone names are usually used on girls like
Pearl,
Ruby,
Diamond, so on… But other than that
Emerald has a nice sound that can be inviting for any gender. For a girl, I vastly prefer
Esmeralda.
https://www.behindthename.com/pnl/217493
"It is not in the stars to hold our destiny but in ourselves." - William Shakespeare