I slightly prefer Alexandria, however at five syllables, it's far too long for me to want to say completely. Whereas with Alexandra, I'd say the full name often.
Nicknames I like:
Lexa, Lexia, Lexy, Lex
Annie, or maybe Anna for Alexandra
Dria, but spelled Drea
Xia is a nickname I had in mind for Alexia, which might work.
I'm not a fan of Alexia for Alexandria because Alexia is such a separate name in my mind that it's like naming someone two completely different first names. Alexa is a better nickname than Alexia, but I'd rather use just Alexa than Alexandria nn Alexa.