AHAHAH, dude, in all that I TOTALLY FORGOT to answer like, one of your actual questions.

Regarding the "nurturing" aspect, actually, no. While "less damaged", Fauxlivia is definitely less nurturing and if anything even more swaggery and masculine than Olivia.

Olivia, on the other hand, is very clearly a defender and protector and has a kind of nurturing parental responsibility towards her niece at various points. She's kind of more characterised as being the a caretaker in various storylines and various revealed parts of her history.