The meaning is not the same. I'm not sure that I've ever heard anyone say 'Who are you to talk?' in this situation, but I would understand what it meant from the tone of voice and context. For me, a more natural response would be something like 'You've got no room to talk!' or a sarcastic 'You're a fine one to talk!'. Both of those sound natural to me, but (standard disclaimer), this usage my vary among English speakers in different regions. I agree with Kenny Lee that 'Who do you think you are?' indicates that you have taken offence at the other person's comment. For example, if a colleague of the same rank as you decides to criticise your work, you might say, 'Who do you think you are?'. The other person has 'ideas above their station.' It means 'You're not my boss and you have no right to comment on my work.' It doesn't necessarily suggest that your colleague's work is bad, but it does mean that you are angry that they think that they're in a position to criticise you. The first is often used as friendly 'banter' between friends, and may be harmless fun. The second may suggest a genuine insult, and may escalate into an argument.

I have heard both. For me as a native of West Coast of the United States I would probably say "Look who's talking! You are just as messy as me!". It has a sarcastic tone. For me, "Who do you think you are?" sounds less sarcastic and more aggressive. I might say "Who do you think you are?" to someone who cuts in line at the store if I am upset.

Both works but "Who are you to talk?" is preferable in this context. "Who are you to talk?" means to point out the hypocrisy of that person's statement "Who do you think you are?" is similar to "How dare you!" and it means to show that you are offended at that person's statement