I know, guys... I know. Darth Vader is beloved by all and there is no way someone could ever be better than him. I don't want to come off as an expert and telling you your opinion is wrong, because that's not my intention. I just want to state some simple facts about Kylo Ren and how he might be more than what he seems to be, because a lot of people seem to have completely ignored or misunderstood his character.
So, in the recent days since Force Awakens came out, people have been disappointed with Kylo, saying stuff like "he's so whiny ! like a kid at a grocery store who can't get what he wants !" and other things like "he's just an emo-wannabe Vader". In some ways, you are right. Before analysing both characters, may you please go watch The Force Awakens, I wouldn't want you to get spoiled about Kylo Ren's surrounding family members and his mental state. Once you've done that, you can come back here.
For the sake of comparison we'll only take the first movie in which each character first appears. That means Star Wars (1977) for Vader and The Force Awakens for Kylo. We'll eliminate all the E.U content Vader has of course. The prequels too will be eliminated, because even if Anakin is technically the same character, he hasn't been dubbed Darth Vader yet (he is named Darth at the end of ROTS, but anyway), so I won't include Anakin's character arc. Finally, we will also take Empire and Return out of the equation.
Darth Vader in Star Wars
Let's take a look at his first appearance and try to imagine yourself there, in 1977, watching Star Wars for the first time, what would you think of him ? "Wow, Darth Vader is so great, with that cool helmet, that black-leatherish cape, that deep awesome voice. And that laser-sword. Wow, he's so cool !"
That's what you would think, be honest to yourself. Next, what do we know about Vader in the first movie ? Nothing, actually. We just have a slightly little hint that he was Obi-Wan's apprentice.
Vader: "The circle is now complete. When I left you, I was but the learner. Now I am the master."
Obi-Wan: "Only a master of evil, Darth."
Other than that, nothing. Not even his real name. We just know he's evil and that he was once the apprentice of Ben. It's only in the next movie, Empire Strikes Back, that Vader gains depth : we see Vader's master (the Emperor), we learn Luke is his son. But as I said, we're only focusing on the first movies. So far, we know nothing about Vader. Now let's look at Kylo.
Kylo Ren in The Force Awakens
Right off the bat, we know Kylo is evil and wants to rule everything as he says himself.
"There is no need for concern. Together we will destroy the Resistance—and the last Jedi."
Not only that, but we also know he's the son of Han Solo and he idolizes Darth Vader.
This is told to us through exposition dialogue. The rest of his character unfolds as the movie goes forward and this time, it has a more cinematic approach.
We also know he's conflicted, he's torn apart between the light side and the dark side. On a side note, let's talk about lighting for a brief moment. In the scene with Han's death, just before Kylo stabs him, Ren's face is lit partially in white and partially in red, symbolizing the internal struggle within his mind.
Doesn't it remind you of any other moment in Star Wars ? Something about Vader threatening to turn Leia to the dark side and Luke being all conflicted... Oh, that's it !
Now back to Kylo. When he finally kills Han, all the light has gone out of his face, now being just pure anger and darkness.
Side note on lighting closed. Let's go back to the character himself. We already know he is Han's son, he's ambitious, he's evil, he's conflicted, he idolizes Vader (wants to be like him). He's also not fully trained, that's why he snapps everytime and breaks everything. Even his lightsaber is a reflection of his lack of discipline. The beam is not focused, it has sparks jumping out of it, like an apprentice made it.
Kylo is also really, really powerful with the Force. I mean he blocks a blaster bolt in mid-air, for Christ's sake ! But wait, you might be thinking "if he is that powerful, how does he looses against Rey at the end ? Explain that." It's really simple actually.
Kylo Ren thinks he's the only force sensitive dude in the galaxy. It's understandable to think that when you have killed all the Jedi (except Luke, which he still has to reach). So Kylo believes he's the only one with the Force and when he gets to Rey, he's not prepared as he has never trained properly against anyone. He has a lot of knowledge on the Force because of his training with Snoke, but when it comes to fighting, he never really trained. Rey, on the other hand, has been on her own all her life. She had to fight a lot, just to survive. But that's not the only reason why Kylo looses and Rey wins.
Let's go back to Han's death. Kylo here, is mentally unbalanced and hurt by that shot Chewie gave him with his bowcaster, which seems to be the most powerful handheld weapon in the galaxy (it kills 3 stormtroopers in one hit). Later, in the last fight, he first comes at Finn, who surprisingly, holds his own pretty well, until the moment when he hurts Kylo. Then, the fight is over in like 2 seconds. He then goes onto Rey, but he doesn't really want to hurt her. This is what he wants :
"You need a teacher. I can show you the ways of the Force."
―Kylo to Rey
He only wants to bring her to the dark side, and if you notice closely, for the whole length of the fight, Rey is running away, until she gets cornered. That's when she concentrates and finds... the Force. Remember she has been alone all her life, doing things by herself, it's no surprise she learns about that herself too.
This is proof of Kylo's strength. If he still manages to fight both Finn and Rey after having killed his own father and getting shot by Chewie, what could he achieve when he's fresh ?
So now that I've laid the ground-work for both Vader and Kylo, I think everyone can start to see why some people hate Kylo, or love him, which is my case.
Those who hate him, they hate him because he's a new character. I don't mean new in the sense that we've never seen him before. We never saw Poe Dameron and everyone loved that guy. I mean new in the sense of a new "kind" of character. They hate him, because they were expecting a new Vader, and of course they were disppointed, because Kylo's character is nothing like Vader. He's more whiny and undisciplined than Vader. Do I need to remind who was whiny ? Anakin and Luke, seems to run in the family. In fact, Adam Driver's performance as Kylo was what I hoped Anakin would've been like in Attack of the Clones and Revenge. Instead, Hayden's performance turned out pretty cheesy.
What I (and I think a bunch of others too) love about Kylo is just that : his difference, the fact that he's a fraud, which I noticed during my second viewing. He walks all tough in front of the troops, but then he's afraid of not being good enough. I also love the fact that he has everything anyone could ever wish for (a Jedi master, a family that cares about him, probably had friends too) but he throws it all away just to be a bad guy, which, unlike Anakin's fall to the darkside, Kylo didn't had anyone to save. That's what makes him so damn compelling. Instead of bad guy trying to be good, we have a good guy trying so hard to be bad.... and he has succeeded. People love Vader, because he's been in our collective memories our whole lives. A new dark, evil character shows up, and people compare it to what they love (which is totally natural) instead of looking for the great things in the new character.
In the end guys, Vader will live on as the biggest badass the galaxy has ever known, but a new kid is slowly taking the prize for being the next biggest badass in the galaxy.