" Honestly speaking " and "frankly speaking " are close in meaning , as in telling the true regarding something .
Honestly /frankly speaking , I hate him .
However, "frankly speaking " is more appropriate in the context of telling the truth, even if it may not be pleasant for the recipient to hear . To be frank to tell it as it is without holding anything back.
How do you like my new hairstyle ? Frankly speaking , ... > You tell it as you see it and not "hiding" any things unpleasant untold.
Honestly speaking , .. > You just tell it in honesty
Being frank is more direct , straightforward and open than being honest when a situation demands as unpleasent reply.