I like Austin - on a boy. On a girl? Meh. Cant say I’m a fan. Austen is only a little bit better. Regardless if I were forced to use Austin at gunpoint I’d use it on a boy, never a girl.
I personally wouldn’t use it because I prefer Augustine/Augustus on a boy (I don’t like Augusta on a girl). Austin doesn’t appeal to me, but if I was forced to use it on a girl, I’d spell it Austen.