Elisabeth, for many reasons.
One, Elisabeth is much less popular than Elizabeth. I think it would be extremely refreshing to see a little girl called Elisabeth, instead of Elizabeth.
Two, Elisabeth has a much softer and more feminine look than Elizabeth. The "s" in Elisabeth makes it seems very elegant and lovely, while the "z" in Elizabeth is harsh and sharp.
Three, while Elizabeth has the nickname option of Eliza, which I like, Elisabeth has the nickname option of Elise / Elisa, which I love.
Four, if I ever used Elisabeth, it would be honouring family, because my great grandmother's name was Elisabeth. If I ever used Elizabeth, it wouldn't be honouring anyone.