I prefer Mariel, but Muriel has grown on me. It sounds strong, quaint, and feminine all at once. I pronounce it MYUR-ee-əl (the last syllable pronounced like the -el in Rachel).
I like Mariel too, but I think I prefer Muriel. :) This is going to sound funny, but I first fell in love with the name Muriel when I heard it on the cartoon show Courage the Cowardly Dog. Haha.