Now that "The Force Awakens" has launched, I want to talk about where Kylo Ren ranks among the pantheon of Dark Side users seen in the films, shows, and Expanded Universe properties. I'll give my opinions, and you all feel free to say what you guys think as well.
Force Powers: Kylo Ren only used three Force powers in the film. Dominate Mind, Telekinesis, and Force stun. Kylo appears to be well practiced in all of these abilities, being especially skilled in the Force Stun ability and Dominate Mind. His combative application of the Force seems rather limited though, as he doesn't really use any of his abilities in combat, only before combat is instigated. He has an unimpressive list of powers, though he can use them very effectively.
Connection to the Force: Kylo Ren is obviously a powerful Force user, every time he uses the Force it is extremely effective (except for when he attempts to dominate Rey's will). His application of Force Stun is incredibly powerful, as he's capable of completely immobilizing his target and even stopping blaster bolts in mid-air. His ability to easily dominate a person's will is impressive at the least, and his Force Pushes seem to be very powerful (he easily launched Rey backwards a good 10 to 20 feet). It seems that, while he doesn't have many powers at his disposal, he is extremely skilled in using the ones that he does know. It's obvious that his connection to the Force is incredibly powerful.
“An incredible power, an incredible force, and incredible potentialthat was, like many young people, sort of misguided and unclear. And the story for him is one of conflict, not just internal conflict but external conflict. And it’s what makes him a rather interesting villain.”
Interview with J.J. Abrams
"Kylo Ren has a lifetime of training and practice, is , and is the leader of the Knights of Ren."
“When next Snoke spoke there was an intimacy in his voice, a familiarity that stood sharp in contrast to the commanding tone he had used with Hux. “I have never had a student with such promise—before you.” Ren Straightened. “It is your teachings that make me strong, Supreme Leader.”
Snoke demurred. “It is far more than that. It is where you are from. What you are made of. The dark side—and the light. The finest sculptor cannot fashion a masterpiece from poor materials. He must have something pure, something strong, something unbreakable, with which to work. I have—you.” He paused, reminiscing. “Kylo Ren, I watched the Galactic Empire rise, and then fall. The gullible prattle on about the triumph of truth and justice, of individualism and free will.”
Taken from The Force Awakens novelization
Durability: Kylo Ren is incredibly durable as well, capable of tanking shots from Chewbacca's bowcaster. The bowcaster, as seen earlier in the film, was capable of sending Stormtroopers flying backwards several feet. At one point a Stormtrooper hit by the bowcaster hit the wall behind him so hard that the wall, as well as part of his armor, shattered where he impacted. Here is a link for reference (I couldn't find the example I was looking for, but this one works just as well.)
Lightsaber Skills: Many people are quick to point out that Kylo is a poor lightsaber duelist, that is simply not the case. For the whole of their duel, Ren was pushing Rey back; dominating the fight. Keep in mind, that he was wounded while doing so; and he was trying to convert Rey, not kill her. His performance against Finn is also something good to point out, as Finn was a practiced hand at melee combat; and even while wounded, Ren was able to easily dispatch him. Ren is obviously not a great lightsaber master, far from the same caliber as his inspiration, Darth Vader; but he is still a competent duelist. I would say that Ren is probably about the same level as TPM Obi-Wan Kenobi or Johun Othone as a duelist, skilled but not excellent.
Personality: Ren is very quick to anger, as seen several time throughout the film. While it's common for Dark Side users to draw on their anger to fuel their power, it's almost always controlled. There are very few Sith, even in the EU, that go into blind fits of rage due to a failure or just getting angry; and those that do still have the skill to stay alive, Ren doesn't seem to have that needed skill. This is another thing that I believe works against Ren, as going into a frenzy can expend energy; against almost any opponent, this would be near fatal.
Overall I think Kylo Ren is competent but not entirely on a true Sith's level. I'd say he's around an average Sith Warrior, such as some of the lesser Sith of Vitiate's Empire. Powerful and skilled, but no threat to any Jedi Master or high end Jedi Knight of note. However, Ren is more than capable of being able to defeat the average Jedi Master.