MrsTwee - Noah is a gender free name, there is both a male and female character in the Bible called Noah, but they are different characters.
Noah of the ark fame was male, it is mentioned that he has a wife, who although is not named in the Bible is named as Naamah in other Jewish texts. He is the son of Lamech.
The female Noah is mentioned briefly (OT), as the daughter of Zelophehad.
One gender free name. Two characters.
However to be honest, in today's modern English speaking world, Noah is seen as being predominately male.
To the OP - I love both names, but as others have said, they're both extremely popular.
Just a suggestion, but what about the name Joah, which you could say combines the two? Joah is a legitimate name, it's Biblical (from the Hebrew name Yoach), and means 'God is his brother'. Said just like Noah but with a J instead.