The biggest things that impact the sound other than frequency response would be soundtsage, timbre, distortion, and comfort.

Soundstage and timbre are both things that are described as being felt more than being heard. That's why just a frequency response graph can't describe the experience of a headphone.

Distortion is an obvious example of a difference of an expensive and cheap headphone. Very cheap headphones will have distortion on some notes even when the frequency response looks not bad.

Comfort might not seem like an aspect that will change a headphone's sound, but it can drastically change the listening experience. An open headphone which barely puts weight on your head can make you feel like you aren't even wearing headphones and getting incredible sound.

I have also wondered what makes headphones hood for a while. I have been in this hobby to know a lot about it, but I am still curious about why some headphone share better. I once made an interesting post where I posted a few frequency response graphs and gave a list of the headphones and wanted to see how well people can match the headphone to the graph. It was to prove that frequency response and tests alone can't give the full story on what a headphone is like. More recently I asked physically what makes a expensive headphone better than a cheap headphone? What are these companies spending r&d on that makes them better? I got a few responses that answered the question, saying it's mainly the driver housing and earcup design which impacts the sound greatly, and they basically use trial and error to find what shape produces the best sound.