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Definitely Cordelia.
I don't like the look for Cornelia nearly as much, nor the sound of it. Plus, Cornelia seems hoity-toity to me, and while Cordelia is an intense name, it feels much more approachable.
I do like Nell, but liking the nickname is not going to make me prefer a name I dislike when there is a full name I do like (which also has nice nickname options) :o)