I haven't heard the D2000, but they are very popular here. You should be able to find a lot of opinions on it.
The K-701 does well with classical, but my favorites for the genre are the AKG K-501 and K-1000, the Sennheiser HD-600 and the Beyerdynamic DT48. All of them have a more natural presentation than the K-701. I think the bes bet is the K-501. It has an expansive soundstage (second only to the K-1000), a very natural and accurate tone, and is fast. Some will tell you that the bass isn't very good, but don't listen. The bass response goes all the way down and is tight and accurate for acoustic material. It does not do amplified/electronic bass well, but it nails a tympani hit just fine. Best of all, you can find a used K-501 for half the price of a K-701.
The HD-600 is excellent all around if you want to listen to other genres. The DT48 doesn't have much soundstage, but it is spookily accurate, quick and lifelike. I prefer the DT48 for solo work and small chamber pieces.