Socrates and Luke are both considered to be great educators. They have both influenced countless people with their teachings. However, comparing the two is slightly strange since Socrates is the subject of the story, which is told by Plato, and Luke is the teller of the story of Jesus. A comparison can be made between the two as Socrates is a great teacher while Plato is mostly silent and Luke, while not overly prevalent in the his story can be compared to other accounts of the story of Jesus among which his by far the most didactic.
But when you are comparing the two you must keep in mind that you are in actuality comparing four and also that while the story teller is supposed to only be telling you what he saw, he is also telling his personal vision of what he saw. Therefore he has a personal bias, which affects the purpose behind his style. A strong parallel exists between the two storytellers Plato and Luke in that they are both biased to a great degree. While they both teach a wonderful perspective they teach solely their perspective with no room for any other.
Luke asserts that when Jesus died the suns light failed; and the curtain of the temple was torn in two, (Luke 23:44) thus giving divine testimony that Jesus is indeed the son of the Almighty. Whenever Jesus is questioned the people who do so are inevitably wrong, there points being made to look stupid as Jesus transcends the question with a new concept. For example, in Luke 20:34-40 Jesus is asked about a wife who has been widowed and remarried several times and to who she should be married in heaven.
This is a difficult question in Jewish tradition where the concept of the resurrection is that of a physical rebirth and the continuation of life on earth. However, Jesus comes up with an new and controversial idea of an immortal soul. He uses the rational that since God only spoke to the living in the Torah, he only deals with the living; so since God still represents you after death, you must still be alive after you die. This is a questionable argument at best however the obvious leaps of logic here are never examined because the questioning scribes no longer dared to ask him another question. Luke 20:40)
This obviously must be because Jesus is the Son of God who speaks with divine and unquestionable authority, or so Luke seems to imply. In much the same way, Socrates also has the authority of the divine. He claims that he is also on a mission from the divine. Apparently a friend of his went to the oracle at Delphi and asked if any man was wiser than Socrates to which the oracle replied that indeed, no one was wiser. (Plato 21a) Therefore Socrates reasons that he is on a mission from the god, as he calls it, to refute this claim.
All the actions that he committed which were considered to be treasonous were therefore demanded by the god, and Socrates had no choice but to comply. This kind or reasoning cannot be argued with since it is backed by a god and consequently it is not. Meletus, Socrates accuser never says a word in rebuttal, or at least Plato never mentions it if he does. Meletus only role for the entirety of the apology is to briefly answer Socrates questions just in whatever way is most convenient for Socrates argument, thus reducing him to little more than a literary device.
The teaching styles of Jesus and Socrates themselves as revealed by their appropriate biographers are themselves nearly identical. In chapter 17 of Luke Jesus teaches a lesson to the apostles saying, Who among you would say to your slave, who has just come in from plowing or tending sheep in the field, Come here at once and take your place at the table? Would you not rather say to him, Prepare supper for me, put on your apron and serve me while I eat and drink; later you may eat doing what was commanded?
So you also, when you have done all that you were ordered to do, say, We are worthless slaves; we have done only what we ought to have done! (Luke 17:7-10) Socrates uses much the same method when he is offering a rebuttal to Meletus accusation that he is deliberately corrupting the young. He says, What follows, Meletus? Are you so much wiser at your age than I am at mine that you understand that wicked people always do some harm to their closest neighbours while good people do them good, but I have reached such a pitch of ignorance that I do not realize this I do not believe you, Meletus, and I do not believe that any one else will.
Both Jesus and Socrates here have both made fairly convincing arguments for some fairly unconvincing points. Jesus tells the apostles that basically they are slaves and they should like it, while Socrates tries to convince the jury that he has done no harm to the structure of Greek society with his radical philosophies. They manage to argue these unlikely lines of reasoning somewhat successfully by leading the listener through a series of progressing questions with very obvious answers until a fairly unlikely, but seemingly rational conclusion is drawn.
Interestingly, this form of education is known as the Socratic method as Socrates was the first to use it. Probably the most convincing teaching method that is used by both the Socrates/Plato and Jesus/Luke teams is martyrdom. Very few things make the concepts that Socrates and Jesus teach more convincing than the fact that they were willing to die for them. Both Socrates and Jesus could have easily escaped death simply by compromising their beliefs a small amount for a short period of time.
However, while there were other motivations involved (i. e. old age and the salvation of mankind respectively) the fact that neither one was willing to compromise their arguments in any way, even when faced with death, gives the ideas that they espouse awesome strength and believability. So while martyrdom may not actually say anything about the truth of what they say, it is very still very convincing.
Overall, it is probably better to look at the teaching styles of Socrates/Plato and Jesus/Luke as being less instructional and more as a form of propaganda. The ways ideas are presented in both the accounts seem to be meant to convince the reader of a particular viewpoint rather than enlighten him. Biased accounts in both cases use manipulative and emotional methods such as leading and fantastic situations to influence the reader. This is not surprising since both accounts are apologies or defenses of a particular view.
The goal is therefore not to educate but to persuade the reader to agree with the beliefs of the author. This is of course not to say that there is nothing of educational value in either of these accounts. Both contain monumentally important ethical principals such as wisdom comes from realizing that you are not wise, and love your neighbor as yourself. However, the actual teaching style that is used by both Plato and Luke is one that has a purpose beyond the readers own education.