Luke Skywalker was a 5'7'' blue eyes blonde hair human. He was born on Polis Massa, and his hometown is Tatooine. He was a member of the new jedi order, new republic, and the galactic alliance. Luke's father was Anakin Skywalker, later known as Darth Vadar. Luke was a skilled pilot and fearless leader. Luke's mentor Ben Kenobi was also a jedi knight. Luke surrounded himself with valuable yet diverse cohorts. The main members of his crew were R2-D2, C-3PO, Han Solo, and chewbacca. Eventually Ben Kenobi would sacrifice his own life for the betterment of Skywalker. Luke had many victories in his quest to bring peace to the universe including terminating the feared death star. Luke's biggest challenge was overcoming his own inner demons. He feared he would be drawn to the dark side much like his father. He hated death, and the immense loss of life that war caused eventually leading him leave the military. Later in life he married had a child and developed the new Jedi Order
James T. Kirk was also human. He was born in space, and lived in all places Iowa. He was the starfleet captain of the U.S.S. Enterprise. Kirk's father sacrificed his life ensuring that James and his mother would survive. Kirk was a brash, and fearless captain. James Kirk had a crew that included Spock, Leonard McCoy and Montgomery Scott. Kirk was a womanizer leading a life of mischief and petty crime until Captain Pike found him beaten and bloody at an Iowan bar and convinced him that the StarFleet needed captains with his never say never attitude. Not wanting to tarnish his fathers legacy, and to prove that the great sacrifice his father was worth it. He joined the starfleet.
Now I have seen one Star Trek movie, and six Star Wars movies. I didn't watch the TV series, or read any books. So I am basing everything on those 7 movies. You have to take away the force. With the force this is a no-brainer, Luke Skywalker wins easily. So if you take away the force you're left with two humans who traveled in time and space to defeat the enemies. You have to take away their crews too. Han Solo vs. Spock would be a great under card.
Hand to hand combat goes to Kirk. He grew up fighting in bars. Skywalker always fell back on the force. Luke has the light saber which Kirk would have no answer to when Skywalker used the force. But again we're taking the force away, so Luke would be left with a sword. And since Kirk is good with a gun, I'll take Kirk.
Mentally Kirk is a rock. He doesn't fear anything. That's what makes him so tough to beat. Luke might have the intelligence to use that against him too. Kirk once got inside Spock's head and forced him to resign as captain of the enterprise, only later to name him 1st officer. So Kirk can beat you mentally. And we all know that Luke is a head case. Luke's best chance here would be to stay controlled and bait Kirk into a overzealous action, putting Luke in a favorable position. But since I've never seen Kirk put in jeopardy, I can't assume Luke would get him there. So Kirk has the upper hand here too.
Weighing all of the options I do not see a way that Luke Skywalker could possibly take down James Kirk. I have to rule that Captain James T. Kirk is the winner.