I've owned all three so I feel I've got some insight to your problem.
My favorite of all three is the hd-650. Out of all three headphones I've kept this pair.
I did not like the K701 very much. It sounded weird and out of balance to me. There was a weird peak somewhere between the midrange and high end that stuck out like a sore thumb and made listening to music distracting because all I could hear was that weird little spike. The bass didn't sound sweet or full or any of the words that I would want associated with my bass. It sounded empty, hollow and without weight. It just sounded weird. I did not like it. But, that's just IMHO.
I'm going to agree with most of the posts about the hd-600 being more neutral and lighter than the hd-650. Although it does sound a bit lighter than the hd-650, it is still an excellent choice for classical. Honestly, I don't remember much from it. Maybe because I realized that the hd-650's took all its strengths and added to them.
Which brings me to the hd-650's, which I'm sure by now you know that I love. They're amazing. Its sound has a weight and it is awesome. That weight adds to texture and contributes to that 'liquid smoothness' someone was raving about. The soundstage is huge and the headphones seem almost transparent. It isn't limited by the drivers or anything like that unlike the K701's. A lot of people think they're veiled, I'm going to have to agree but the highs are there make no mistake! I got a zu-mobius cable that helped take some of that veil off which helped a bunch.
I agree with that other poster about having a good setup to get everything out of the hd-650's. I've got a bel Canto Dac-1 and a nice SP tubeamp coming out of a cheapo sony cd player (cd595?) that have a lot to do with making this headphone.
If you've got the goods, go for the hd-650.
Great advice in this thread!