Quite honestly, it's a toss-up. I go through periods when I use the HP-1 a lot, and others where I'll listen to the R10. I have other headphones, but one of those two is always my primary.
The R10 excels at imaging. Big broad image, with a resolution that no other dynamic headphone touches, IMO. The weaknesses are the bass response. While bass quality can be very good, even at best it sounds as though the bass player has stepped to the rear of the stage. At worst, it can sound like the bass player fell off of the stage entirely. The other "weakness" may be part of the appeal as well. The R10 is not a neutral headphone, nor has it ever pretended to be. It has a very distinct sonic signature that it imposes on the music. This is a very euphonic coloration, and very pleasant to listen to. When it's "on" the R10 can do magic. The R10 is very finicky about amplification, despite being a fairly efficient headphone. If the amplification is off, the soundstage can sound compressed, and the coherence of the sound will come apart.
The HP-1 (HP-1000 series) is probably the most neutral of the dynamic headphones. It was actually designed as a studio monitor, but makes a superb consumer headphone as well. It doesn't have the imaging capability of the R10, but doesn't impose it's own coloration on the music either. It's a relatively inefficient headphone, but still within the range of most headphone amps (only the K-1000 is less efficient in my experience). In some setups, it won't seem to have as much detail as the R10, or even the subsequent RS-1. It appears to be far less dependent on the amplifier than the R10, and will sound good with most amplication. This is partly illusory, as the HP-1 will respond to changes in amplification and cabling, and reach levels of performance that can be absolutely stunning. I suspect that the less finicky nature of the HP-1 may lead some owners to not realize just how good the headphone can be, just because it sounds good without maxing out a system.