I think I might disagree SLIGHTLY with mg2550arch on the Beyerdynamics DT770's use for Classical music.
I modded mine, VERY SLIGHTLY, by removing the foam that covers the speaker screens inside the cups and the clarity improved quite a bit, the bass seemed less muffle-y. After substantial burn-in, the clarity of the bass range improved very nicely.
I think the more bowl shaped build of the K550's helps increase sense of stage right out of the box.
I am also going to see what happens with some Grado g-cush as a mod in regards to increasing the bowl on the Beyers and still keep the closed back isolation.
I prefer how well the Beyers exclude environment noise when I am stuck in a situation with racket nearby.
(I'm an ER physician and sometimes have to sleep in a call room immediately adjacent to the ER itself....)
I chose the Beyers over the AKGs for this reason. And the versatility, as you say, is a bit broader for the Beyerdynamics.
As said, it's about taste and situation.