Both names give me a completely different feeling; and I don't think they're even related except for sound. I'll have to go with Emilia; 1) it's Shakespearean, 2) It looks better IMO, and 3) I don't really like Amelia.
DittoI like them both, actually, but agree that they give me a different feeling and aren't supposed to be related by anything except sound. Click the blue link - this site also claims that Amelia is off of the Germanic Amalia. I didn't think it was Roman.