I think they're both dated. I used to live in Germany and there were lots of women named
Anya (mostly spelled
Anja) who were born in the 70s.
Anna is very 80s dated, but I think it's also dated here in the US. I think I prefer
Anya. I like the spelling that uses the Y instead of
Ania or
Anja. So
Anya looks pretty to me.