I love the V6's, but honestly, there's no comparison. About the only thing better with the V6 is some ruthless detail and decent isolation. The bass is a monster in the V6. That's good in some circumstances, and I love it in many ways and will probably never get rid of it.
However, the HD580 is just on another level. Bass is almost as strong, but runs much deeper, cleaner - and with detail. Compared to the V6, the highs are a little recessed, but that allows a beautiful, warm midrange to come through - something almost entirely absent in the V6.
Then there's the fact that it's an open headphone - the music will open up compared to the V6, but it won't lose impact. That's difficult to imagine until you've tried it, but it's true. At the same time, everyone in the room will hear it, so keep that in mind.
Finally, the comfort is just unparalleled for a headphone that's large enough to completely cover even the largest ears. The headband is unbelievably comfortable, too. Just superb comfort is present all the way around.
The only thing I'd disagree with somewhat is this discussion of unamped/soundcards/motherboards. While it is true that the HD580 can be played without a good source or an amp, you'll want to pursue those as soon as possible. Far from a disadvantage, you'll find that it will continue to improve in sound quality with everything you throw at it - swallowing $1000 amps and saying, "give me more." Yet, a reasonble CMoy with proper attention to voltage (2-9V batteries are best) can overcome much of the power threshold in the Senn - the rest is in detail and subtlety (lots of it to harvest, though!).
On the other hand, the V6 is adequate with the voltage from portable players: only the bass tightens up with a good amp. Unfortunately, amped V6-highs may form daggers into your skull, while the midrange voices can become shrill.
Personally, I think a headphone that can grow with your tastes like the Sennheiser HD580 is a very worthy investment. Certainly - as one of the best headphones ever made, every headphone fan should purchase one.