Actually I think 'don't get me wrong' is a softer and gentler thing to say. It is said in a tone almost of excusing oneself for fear one's words would give the wrong idea. . By contrast 'don't misunderstand me' is more aggressive, the implication is that it is the listener who would make the error of misunderstanding. "Don't get me wrong, I think kids are great. I just don't choose to have any of my own." "Don't misunderstand me. I'm not saying this to be mean, I'm just pointing out your mistake to help you learn."

'Don't get me wrong' is an informal way of saying 'don't misunderstand what I mean'. eg Don't get me wrong, but I am sure I have seen you at this restaurant before. eg Don't misunderstand me, but haven't I met you somewhere before?

although almost same in the mening don't get me wrong implies a negative sense that the speaker is a bit disappointed; while don't misunderstand me suggests that there was a differencce in following the speaker and this difference may be both positive and negative.

hello aqua, in my opinion, both statements are suggesting that what you have said or done should not be misinterpreted or taken falsely. although "don't get me wrong" is quite often used than "don't misunderstand me", they literally imply the same meaning. the only little distinction i see is that "don't get me wrong" is a bit aggressive and stresses command to the one you're talking to. "don't get me wrong, I'm here to get my things, not to confront you!"