I think King tends to focus on the ordinary people of the stories, even allowing that the ordinary people might actually just be deranged versus affected by the supernatural, while Barker features the supernatural as his participating characters.
In The Shining, every single action taken by Jack could have simply been the deranged effects of severe alcoholism. The visions, the interactions with the supernatural, all of it could have really been entirely in his head. And that made it even scarier. (King didn't like the Kubrick movie version for that reason, but I think King sold his fans short. I actually I liked the visualizations of his delusions, and I didn't see them as supernatural at all! I knew they could have all been in his imagination, and also in Danny's, as a child's mind reacting to the father's alcoholism).
Meanwhile, in Hellraiser, the Cenobites are active characters in the story. They are essential and "real" characters affecting Frank, then Kirsty and her family. There is no way they could be imaginary.
As King's writing evolved, he got more into the idea of normal people doing very evil things, sometimes affected by the supernatural or evil but ultimately regular people making the right or wrong decisions by themselves. Readers can associate with those characters more easily, because they imagine it could be them being affected by it. (e.g., you are Paul in Misery, suffering under the total control of a deranged "fan").
Barker's fiction tends to frighten based on the blending on heaven and hell. It's a fun adventure, but we still know in our heart that it's make believe. And the intense and violent sexuality of some of his themes can be too much for some readers. He likes that, he wants you to cringe. But if you're not into that, you quickly get turned off.