who gives better logical arguments Socrates or Dr.King. why?

Socrates of course. Why? Because he basically used the best method of all, challenging his students to come up with answers, right or wrong.

Whereas Dr. King used peaceful demonstrations, and to a large extent copied Gandhi's theory of civil disobedience, Socrates wanted to challenge the thinking of his opponents. In other words, force them to come up with critical thought and then use that dissonance to find a solution to a problem.

Hence, the Socratic Method. This method is long-enduring from the time of Socrates until now.

1. Thesis or theory is stated by inquirer.

2. Respondent then responds with his/her own viewpoint whether agree or disagree.

3. Inquirer then challenges the agreement of the Respondent, pointing out flaws and forcing the respondent to defend his/her position.

4. This continues until the Respondent contradicts him/herself.

5. When contradiction intervenes, then the inquirer shows the Respondent the flaw, and then forces the Respondent to propose a new thesis which is again tested in the same manner.

Eventually a solution or "best answer" is determined and perhaps the issue is solved, or it remains an unsolved question.

Socrates.

King did not give logical arguments. He appealed to the emotions and got people to agree with him on a gut level.