The novelization of Star Wars: The Rise of Skywalker suggests Kylo Ren never really understood Darth Vader at all. When Kylo Ren was introduced in Star Wars: The Force Awakens, he was clearly obsessed with his grandfather. Kylo Ren saw himself as the embodiment of Darth Vader's legacy, and believed his goal in life was to complete the Dark Lord of the Sith's mission. It was never entirely clear what Kylo Ren believed Darth Vader's mission to be, though.
No doubt Kylo Ren was fascinated by the apparent parallels between his own experiences and those of Darth Vader, but he was blissfully unaware this was simply because they had both been manipulated by Palpatine. The Emperor was actually less successful with Ben Solo than he had been with his grandfather, because Ben saw himself as trapped by the dark side rather than seduced by the lure of its power. It's notable that, in Star Wars: The Rise of Skywalker, Kylo Ren told Rey to "surrender" to the dark side - unwittingly hinting at his own relationship with it, one of conquest and defeat rather than choice.
Rae Carson's novelization of Star Wars: The Rise of Skywalker goes further, implying Kylo Ren never truly understood Darth Vader at all. In one early scene, Kylo Ren strides through Corvax Fen, one of the few patches of life on the planet Mustafar. He considers why Darth Vader would call this planet home - and gets it completely wrong.
"Kylo Ren showed mercy to nothing and no one, but he had a grudging appreciation for things that struggled to survive. Even though the nearest lava flow was many klicks away, it seemed as though the air ought to be too hot, too chemical, for life to truly thrive here. As they'd landed, Hux had proclaimed the planet a 'desolate hellscape,' and Kylo hadn't bothered to correct him. The truth was, Mustafar was teeming with life - all connected through the Force. Like those hapless cultists he'd just killed, who'd been obsessed with protecting Vader's legacy. Or this forest of twisted irontrees they endeavored to cultivate. Or even the extremophile organisms that swarmed the lava flows. All fragile but determined, mutilated but indomitable.
It was no wonder his grandfather has chosen this place for a home."
In reality, of course, Darth Vader had a far more intimate connection to Mustafar than Kylo Ren appears to have suspected. This planet was rich in the dark side of the Force, and as such Darth Sidious chose it as one of his main bases during the Clone Wars. In Star Wars Episode III - Revenge of the Sith, the newly-christened Darth Vader headed to Mustafar to slaughter the Separatist leaders. He was pursued there by Padmé Amidala and Obi-Wan Kenobi, and in a moment of anger Vader killed his beloved wife. He then dueled Kenobi, and was left critically wounded, with Palpatine forced to transform him into a cyborg in order to keep him alive. In a sense, then Mustafar was the planet where Darth Vader was truly created.
The Emperor originally sent Darth Vader to Mustafar in order to torture him, to force him to confront the demons of his past. But Darth Vader swiftly found another reason to call Mustafar home, when he learned of legends of a Mustafarian gemstone called the Brightstar. As revealed in Oculus VR's Vader Immortal game, the Brightstar could be used to perform a dark side ritual that would resurrect the dead. Darth Vader hoped to acquire the Brightstar and resurrect Padmé, an act that would potentially have been possible, but would have required the sacrifice of the entire planet. Far from impressed by Mustafar, Darth Vader lived on the hellscape because he saw it as a means to an end - nothing more. Kylo Ren's failure to appreciate this suggests that, for all his knowledge, he had fundamentally failed to understand Darth Vader at all.