Essentially none in this context. But, as I explained, when constructing the sentence with the past participle (född) you have to use present tense (är född) for living people and past tense (var född) for the ones no longer living.
Is the reason that "Jag är i juni född" is wrong because predicate adjectives need to be immediately after the verb? Or is there a different reason? (I think I did it this way out of German instinct for the equivalent sentence)