I prefer
Aubrey. I like
Audrey very much, but I try to imagine saying
Audrey 50 times a day to a three year old, and that Aud- ("odd") first syllable begins to grate on me.
Aubrey sounds more pleasant, imo.
I haven't read the other responses yet, but I'm sure it has already been pointed out that
Aubrey and
Audrey share a similar sound, but they aren't actually related. The have different etymologies and histories. Sorry to be repeating something you've probably already been told, but my namenerdiness demands I say it again just in case.