According to the (Google Translated and then more carefully picked apart) blog post where she was introduced, there are some differences of note between the two:
Alice is shorter(?) than Emilia
Alice is slender where Emilia is curvier
She has a sadistic personality
She is not as emotionally mature as Emilia (Or "has a more childlike mindset," possibly)
"If Emilia's kicks can be thought of as 'a whip or a blow from a (hammered) spike', then Alice's kicks are 'a scythe or the slash from a spear'." (not 100% sure of this)
"Alice is like Guile, while Emilia is like Chun-Li."
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