I just think it's nicer; not because of religious connotations, on the surface.
But if we're talking about the religious associations...
That seems kind of like
Azrael vs
David. One is more obscure than the other, biblical
David did some sketchy things, but I don't really associate the name
David with being an adulterous peeping-Tom, the way that
Azrael seems associated with death and supernatural beings.
Lilith is more obscure than
Eve, but all
Eve did was trust a reptile by eating an apple.
Lilith was supposedly a demon who killed kids.
Eve is basically more like the whole world's mom.