What you're describing is technicalities vs frequency response. How "good" a headphone or whatever is; is down to a combination of frequency response and technical performance. But technical ability can't really be measured in as simple a way as frequency response, so it's more subjective. Also, how importantly you weigh one over the other is also subjective and down to your personal experience/taste. EQ is very powerful and I think everyone should use it, but it's also true that FR isn't everything. If it were, you would be able to make two audio devices sound EXACTLY the same with nothing but EQ, but that really isn't possible and that becomes obvious to anyone into the hobby for a while. The remaining portion is loosely described as "technicalities". There are ways to measure aspects of technical performance but like I said before it's a lot more subjective. I think most would agree though that technical performance is almost all down to driver type, material, configuration, surrounding assembly etc. Basically, the moving mechanical portions of the audio device that actually produce sound, and the parts that effect them. It's also worth noting technical performance doesn't necessarily mean the same thing as "detail", since the perception of detail can be greatly affected by both technical performance and FR.

There is way more to this topic so I would suggest you look more into the science and engineering aspects of audio if you want to know more.

For someone just trying to buy headphones though, the FR graph is a good way of understanding how their own preferences are visually represented, and how measured devices line up with those preferences.