Abrahms and Trek Spoilers ahead:
I am not so sure about the first movie, but the second had a message - Kirk was basically willing to give up Starfleet principles for a moment, and then did not, instead of assassinating someone without a trial, he brought him back the Federation and trying to figure out what was really going on. Th
We've seen Kirk doing something similar before, too, in the original timeline - Startrek VI. He hated the Klingons for killing his son, and wanted them to die - but he did in the end fight for the peace treaty and stop the conspiracy to halt the peace treaty.
And in both cases we had members of Starfleet that have sworn to protect the ideals of the Federation betraying them, believing that was the only way to protect it.
So there are two "moral lessons" here, that both seem relevant in our time:
-We cannot allow ourselves to be blinded by a thirst for revenge and let us forget our principles.
-We must be careful that we do not to sacrifice the ideals our society is build on in our attempts to protect that very society.
Interestingly, the second lesson particularly is also something touched in DS9, my favorite show of all Trek series, and the favorite episode of many DS9 fans - "In Pale Moonlight", in which the conclusion is different. Sisko was able to accept having lied and aided murdering someone against any Starfleet ideals, if it meant saving the Alpha Quadrant and the Federation. (But make no mistake, DS9 also made the opposite point, particularly in regards to Section 31).