As a general rule upper double chromatic approaches that begin on a non-diatonic note are very dissonant and usually avoided. The other issue is that they create modal ambiguity. In the case of the 3, if we start a dch from above we are starting with the #4 which is not diatonic to the mixolydian. As a result, the sound produced is associated with the lydian,lydian dominant or super locrian.
So, if you want to play it safe, the best sounding double chromatic approaches are those that begin on a diatonic note.
Let me know if this answers your question.