Well, I personally think it's hard to compare these headphones because both the K 701 and HD650 are quite different from the HP1. The HD650 sounds more like the K 701 and vice versa than either sound like the HP1. And personally, I think the HP1 is a difficult headphone to describe. But here goes.
Oh, I'm assuming you're using the HP1000 with flats. I'm also much more familiar with the HD650 as I've owned them from time to time, while I've only heard the K 701 on occasion.
Both the HD650 and K 701 will give you a wider sense of air than the HP1. Their sound will seem to be more diffuse spatially, perhaps more pseudo-speaker-like might be a way to describe it.
To my ears the HD650 and K 701 have greater extension on both the highs and lows than the HP1. Treble will seem more crisp on either of these two cans.
Neither of these cans have the purity of tonality that the HP1 does. In other words, you will always be aware that you are listening to reproduced music, at least with most normal amps (some amazing systems can draw some amazing performance out of these cans). The HP1000 has the remarkable capacity for the drivers to just disappear, leaving you directly connected with the music, and neither of the newer cans can do that, at least in most systems.
Hmm, I suppose I could go on forever the more I think about differences... but I guess there's a start. Honestly, if you're looking for direct-fire timbre, impact and resolution, the HP1000 is the way to go. If you want a more spacious soundstage, more extension, and perhaps, arguably, more technically proficient/nimble performance - though, surprisingly, this doesn't always translate to a more rewarding musical experience, at least not without quite a bit of work, I guess I'd look to the newer cans. My preferences are strongly for the ancient Grado, but the newer cans have much to recommend them.
Best,
-Jason