I think they are both lovely names. I think that for people whose age is already in the double digits, Anna seems like a "common" name, b/c they probably have a host of cousins, aunts, etc with the name. However, it seems as though usage of Anna (and I could be wrong about this) has tapered off in the last decade or so...I think it is a nice choice. Whereas Juliana and Julia, it seems, has been used more frequently as of late.'
best of luck!