"Mi" is an affirmative marker. It makes it a little more explicit that you're using the positive form and not the negative form. ("Mi" also causes a soft mutation, but that wouldn't affect "Es i", so you don't notice it here.) I don't think it's any more correct, or even more emphatic; it just makes it harder to miss the distinction in speech.
I wonder whether the similarity of the particules mi, fe to the pronouns mi, fe is coincidence or not!
As far as I can tell from GPC, those preverbal particles did come from "I" and "he", respectively, originally but later lost those connotations and came to be used for all persons.