However, to suggest that the show is better than the books is crazy. If you had read the books before watching, you could see it really going off the rails in season 5 (some would say season 4) and it kept sinking lower and lower as we went on until the disaster of season 8. Sure, the show could provide awesome visuals rather than relying on words jumping off a page, so maybe a story like Game of Thrones is more suited for a visual medium, but the story in the books seemed so obviously superior to the one in the show.
Daenerys is an absolute disaster of a character in the show, especially season 8. We had various characters tell us that she was going crazy before the show actually showed us. It was a perfect example of tell not show (the opposite of what you're supposed to do as a writer). It's as if many scenes got cut. I have a hard time believing GRRM would be that sloppy on something so basic. His first-person perspective of Cersei's descent into madness may have been a bit ham-fisted, but it was still understandable. I'd assume he could do the same for Daenerys.
No, the books don't take a deep dive into the psyche of a single character like one of those other authors (supposed literary greats, I've never read their works, so I can't comment) might have. However, what we did get was at least waist-deep into their psyche so that we could understand them. We could understand how they act in a brutal world of conflict and magic. The characters who got perspectives didn't seem flat to me at all. They were actually quite nuanced. They had understandable motivations and internal conflicts that resulted in a mix of decisions with natural consequences.
If you really want to get deep into the ASoIaF world (go to youtube and watch Preston Jacobs if you want to go down that rabbit hole), there is an extreme amount of symbolism and an interconnecting plot that runs through many different storylines... something that I don't think too many of those literary greats have attempted. Having said that, most people guess that GRRM is having a hard time reconnecting some of those plotlines in a sensible way to get back to the points he is trying to hit. However, the struggle goes to show the care that is put into the books and that he's not just going to smash pieces together and call it a story like D&D did.