Personally I think they're too close. When you write them one after the other you write Beth twice. I know a family with a Stephanie and Stephen and that's too close too. But they are nice names.
I think it really depends on what Elizabeth gets shortened to. If she gets Liz, Liza, Libby etc., that'd work fine, but if it's Beth... you might end up with 2 girls who get called the same thing.
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