This is what I wrote in another thread when someone asked for a comparison between the K400 (relative similar to the K501, but more bass), and the K601:
f you listen to the K400 from a hifi perspective, I don't think you hear anything that stands out. It's more the organic feel they give, it's a pleasure listening to music with these cans. They are very balanced throughout the audio spectrum. Musical is the word that comes up.
Balance, mids, highs, they're all integrated in the sound.
The K400 is detailed, but not too much. Mids are slightly forward, yet warm at the same time.
The sound of the K400 is quick, and a little bit lightweight. Toe tapping is guaranteed.
They excell with female voices. For example listening to Emmylou Harris is a real treat.
Bass is not deep, but very tight.
Sibilance is very tolerable
They can handle al lot of styles: pop, country, folk, some rock.
Not all kinds of rock. For example, the band Rush sounds awfull with the K400.
Than it's time to grab the K601. The 601 has more body, slam, oomph, or how you will call it. They are even better with all kinds of music. But they are not as airy as the K400, soundstage is smaller.
I think the treble of the K601 is more rolled off. But still the K601 is very detailed and revealing.
The K601 sounds slightly warmer/darker. The bass is a little thicker, fuller and slower.
The K400 wins on PRaT. The K601 gets my feet also tapping, but less than the K400.
The K601 wins on impact, authority and presence with heavier rock. It's more a all-arounder.
They're both very comfortable.
It's hard to say which is better.
They just sound different, and useful with different kind of music.