Perhaps better than any other Star Wars film so far, the lightsaber duels in The Force Awakens tell a story and establish who the characters are in that moment. Only the duel between Luke and Vader in Return of the Jedi even comes close to telling this sort of tale via clashing blades. At first glance, the duel between first Kylo Ren and Finn and then Kylo Ren and Rey is brutal and it doesn’t get any less brutal after repeat viewings. Gone is the elegance of the Prequel Trilogy and with good reason. Kylo Ren doesn’t have the benefit of training with a Jedi Order who has perfected the weapon over millennia and Finn and Rey have never even held a lightsaber before that day. Every swing of a saber has meaning and you don’t need to have seen a single other frame of the film to get what sort of people these three characters are.
Finn has the least training with these sorts of weapons and it shows. He gets in a few good blows but it comes off as more beginner’s luck combined with a Kylo who is far from being at his best. (More on that last part later.) With any sort of sword fighting, a raw beginning can sometimes have more luck than someone who has trained, as they do not react in a way that is expected. In other words, someone who has even basic training will be more likely to attack and block in a way that utilizes more standard stances and responses that will be easier for someone else with even more training to counter. Unfortunately, it’s just not quite enough to help Finn last more than a few minutes despite his determination to help his friend.
Kylo Ren’s responding actions speak louder than any words could. He doesn’t take Finn as a serious threat. A traitor? Sure but he’s clearly familiar enough with Hux’s training program to know that there’s no way FN-2187 knows enough to be more than a nuisance and it shows. He toys with Finn especially at the start, dodging some of Finn’s more wild swings with a distinctive ease and even knocking him to the ground and turning away instead of pressing his advantage and ending it. Turning your back to an enemy is an insult. It’s not until Finn lands a blow that actually hurts him that Kylo steps up his game and decides to end the fight now. This time, he’s not content with disarming Finn and follows it up with an injury that ensures the former stormtrooper will stay down.
On the other hand, Rey is a bit more prepared for this sort of fight. Throughout the film, we see that she has experience with pole arms. She’s more than competent with the use of her staff and quite handily took down Unkar’s thugs. However, there’s definitely a difference between using a sword and something that’s more akin to a quarterstaff and it’s a handicap against her. Rey has enough skill to force Kylo to treat her as more of a threat but up until a very specific turning point, he clearly has the upper hand and forces her to consistently retreat. When confronted with Rey, Kylo’s style takes on two new aspects. He’s not only more aggressive and intent on winning the fight but he also gets a little more erratic. Apparently rejection and having a giant hole in your side can do that. It is also here that we can see that his mental state is wavering thanks to the occurrences of the last few minutes.
Everything completely changes for both combatants after their “You need a teacher! I can show you the ways of the Force!”/“The Force?” exchange. Rey centers herself and every one of her subsequent strikes are focused and calm yet aggressive. She doesn’t feel quite as in over her head. Now she’s the one on the offensive, forcing Kylo backwards. In contrast, Kylo loses it. Any focus he had left vanishes and everything about his fighting style (or lack thereof) telegraphs that this is a man who has, within the last hour, murdered his father, been rejected by his family’s lightsaber, been shot in the side with a bowcaster by someone who was probably like an uncle to him, and who is now being beaten by a scavenger with no Force training whatsoever. His swings become more wild and desperate even as hers show more control. Both of their actions speak louder than words ever could. By the time Rey strikes the final blow that scars Kylo’s face and makes him stay down, it is beyond clear that he is broken while she is strengthened by the discovery of the Force. No one needs to say a word because of how perfectly every blow conveys who Rey and Kylo are in that moment.
The beauty of these roughly six minutes doesn’t come from acrobatics or the rush of seeing two former friends fight each other for their very lives. It comes from the story that is told, often brutally, through every single strike and parry. Without a doubt, it is an achievement by the fight choreography team and we will watch the lightsaber films in the next two films with great interest.
While I agree with your overall theme, I think it’s incorrect to say Finn has the least training – I’d argue his training with a mace (see Star Wars: Before the Awakening) is more akin to using a lightsaber than Rey’s, albeit much more honed, abilities with her staff. I think it’s more that Finn is scared, and Kylo can see, can feel it, and he uses it to his advantage, toying with Finn until, as you said, Kylo allows a strike through his guard and decides it’s time for no more Mr. Nice Guy…Rey, on the other hand, fights with an instant confidence gained from calling the lightsaber past Kylo and to her, a move that simultaneously enrages Kylo, allowing the dark side to swell within him, giving his attacks more gusto than he’d previously shown with Finn…
So, while I think it’s more a matter of emotions than training or ability, I do think the two battles tell a wordless story that is not to be simply chalked up to an action-packed fighting scene…