in general:
701's are bright, airy, and very forward. They sound like you are sitting in the back row, yet everything is still very strong and clear (this 'artificial contrast' prevents me from calling it neutral or transparent it always sounds like this). Gives it the airiness and soundstage. The extreme clarity gives the impression of reference sound. The 701 have very light/thin drivers giving good dynamics and accuracy. However this is also a shortfall because it will sound lean and lack the 650 richness. I think i'll admit that the 701 can go deeper than the 650 though just without the weight and fullness. The 701 IMO doesnt need a crazy amp to sound good. The first thing is high gain because it takes more than the average volume to get sound out of it. Then a more powerful amp will give it a little bit more weight and finesse. I thought the 701 sounded pretty good right out of the Pico.
IMO the 701 is a piercingly bright can when new. Must break in...I've had 2 virgin K701 in 2 months. i got rid of my single ended one after ~400 hours and i just bought another balanced one.
the HD650 is 'naturally' a dark headphone out of the box (colored but correctable might be a good description). It puts you in the frontmost rows (unbalanced) balanced sounds like midrow with larger soundstage, depth, and much more layers than even the 701 balanced. Things sometimes sound really distant and it will detract from the clarity (people call this the 650 veil). It is very rich/heavy/syrupy sounding...so much that it sounds slow and maybe even overflowing into the other frequencies when not amped properly. The 650 is very Smooth, and virtually never harsh on the highs. The 650 is VERY sensitive to component changes. Give it a bright source, silver cabling, and proper amp, the headphones will turn bright. Use the wrong stuff and you can make it sound really bad. Point is with the right components you can get it to sound really really good. MY 701 sounds good, but not as good as my 650...I'll admit the 701 sounded much better before i got the Big amp which is supposedly factory tuned with the 6x0 in mind. The balanced HD600 might be better for you if you dont want to go this crazy.