Well, both have meaning that are very similar. "Frankly speaking" sounds more blunt and if more often used in negative situations when one is going to talk of a problem, etc. "Honestly" sounds less harsh and is used in more informal settings (with friends for example). But their meanings are very similar. Hope this helps!

For both of these, the meaning and the speaker`s intention comes from HOW THEY SAY IT i.e. their intonation as well as how fast or slowly they say it, are they smiling or do they look serious... There is no difference in meaning between these two expressions...they`re both just phrases to signal that the NEXT PIECE OF INFORMATION is going to be disappointing or surprising to the listener... For example: Bill: Do you want to go for pizza later? Jennifer: HONESTLY, I'm feeling a little tired. Maybe next time... - - - - - - Or, maybe a speaker expects that the listener will think their opinion is too strong / surprising / in contradiction, and so, to soften the difference -- the speaker signals that what she is about to say is suprising... John: What do you think of the government plan to build a lake in the middle of Toronto for the G20? Sally: FRANKLY SPEAKING, I think it's a waste of taxpayer money!