I prefer
Elsa. You could also name her
Elisabeth and nickname her
Elsa. I think I prefer
Elsa on its own, though. It has such a nice sound and isn't so long and not so common.
Elisabeth is beautiful but very popular. The thing is that you get many nicknames from
Elisabeth:
Liz,
Lisa,
Beth,
Betty,
Elisa,
Ellie,
Lily etc which is nice and you just get
Elsie from
Elsa. Still I would go with
Elsa :)