Actually this sort of getts answered in the last few volumes of season 1
Personally though, they're both the same personality, just different sides of it. Without the rosary moka is a full blown vamp with all of benefits and downsides. When she wears the locket part of her conciousness is sealed, which led to a new type of personality.
It's not the first time we've seen this type of thing, Mahoraba Heartful Days used a similar premis aswell.