Frequency response graphs show how a particular transducer outputs each and every frequency given the same input level. You can pretty easily tell if the headphones are bass-heavy, warm, balanced, or bright.
Take this graph, for instance:
The Sennheiser HD650, HD595, and HD555 are being compared. They are all relatively close in their frequency response, but will sound quite different from each other if you listen to each of them.
Frequency response graphs won't tell you anything about the soundstage, tightness, dynamics, or clarity. This is where most of the debate happens. While pretty much everybody can agree that headphone X has a lot of bass, some will feel that it has too much, while others feel that they need more. Some might feel that the bass needs to be tightened up, others might feel that it's great just the way it is. There really isn't a good way of measuring these characteristics, since it's mostly subjective at this point.
It also depends on what type of music you listen to. Somebody wanting cans that are great for classical music will desire something completely different from somebody who listens to rap.
Not only that, but everybody's ears perceive sound in different ways. As it is, we don't even hear sound exactly the way it really exists around us. Human ears have a natural spike around 3,000 Hz, meaning we perceive sounds at this frequency as being much louder than at other frequencies, even if they're really being played at the same sound level. We also have a roll-off at very low and very high frequencies. But again, everybody's ears will be different.