My choices would be:
Louisa - I think the "a" ending makes it more feminine and less old-fashioned. Louise always makes me think of Thelma and Louise.
Amelie - I do like Amelia a lot, but it is getting popular. I'm never sure if I'm saying Emilia correctly.
Alexandra - I prefer this classic name over newer Alexa and Alexia.
If you're asking for my favourite of the group, I'm torn between Louisa and Alexandra, but I think I'd say Louisa as it's not very common.
Louisa vs Louise - Louise. Sounds simpler and prettier to me.
Amelia vs Emilia vs Amelie - I'd have preferred Emily over them all, honestly. But if choosing between this three, I pick Amelie. Emilia is a boom name in my area and I am pretty tired of it (p,us it sounds unbelievably horrid with typical for my country last names and patronymics, I can't understand why to this to a child - think Emilia Petrovna Ivanova) and Amelie is more charming than Amelia.
Alexandra vs Alexa vs Alexia - Alexandra. Alexa sounds like boys name with -a, weird feminization to my ears(a la Adama or Davida) and Alexia, if I am not mistaken, is a medical term.