Brittany is fine. It's a nice part of
France and even though it is called Bretagne in French I like the connection.
Brittany also looks fine to me, even though it is a bit girly/cheerleader-ish. I am not crazy about it because it used to be so common and seems a bit cutesy but it's fine on someone else or for someone elses child.
Britney on the other hand reminds me only of
Britney Spears and as it isn't spelled like the region it seems more unauthentic/trendy/dated.
Overall I prefer
Whitney which seems classier and less cheerleader-ish but
Brittany is perfectly fine overall.