Other native speakers might have different opinions (it might be a question of where you're from!) but to me they both mean more or lesson the same thing. I'd say they're both correct in spoken English (although I would always say 'I'll' instead of 'I will') but 'I'll have it done by Friday' puts more emphasis on the completion of the action. I feel that the first option sounds a bit more relaxed, whereas the second one carries a bit more weight; it might be in relation to a deadline or something, and you're confidently telling your boss that it'll definitely be done by Friday!
Hope that helps :)