I love both names. It depends on what affect I want to give.
Elizabeth is strong and regal.
Elisabeth is soft and romantic.
My very, very, very favorite nn is
Elsie /
Elsa. Adore it. Others I love:
Bess,
Bette,
Betty,
Betsy,
Libby,
Lee,
Lily (except it's getting too common),
Lilibet and
Lizzie.