Let me preface this by saying that I have not heard the HE-6.
One of the issues in comparing speakers systems to headphones us that you are getting a great deal of reflected room sound with almost any speaker system. There are pluses to that that reflected sound but it is time delayed and out-of-phase. Near field listening (six feet/two meters or less) reduces the impact of this phenomena. In my experience smaller monitor speakers end to be best suited to near field listening. Generally speaking I don't think line source or horn systems tend to work well near field. Some planar speakers do very well in the near field, the old Stax ESL F81 or the original Quad ESL are examples, but not all. The problem with small monitors, especially really small monitors, is that they lack both bass impact and extension. Subwoofers can partially address this but if the main speakers don't gave fairly solid performance down to at least 50Hz - 60Hz is is quite difficult to achieve seamless blending. Also, if you're missing mid bass, as opposed to low bass, impact a subwoofer is not a good solution.
As to which speakers have great mid range and mid bass performance I think planars are tough to beat: Soundlabs, Quads (I only know the originals and the 63s but the Chinese built newer Quads receive very mixed reviews for quality control), Stax, Beverige and Acoustats (the full range models not the hybrids) are all capable of great sound with the right amps. I also like the planar magnetic Magnepan and Apogee speakers. If you're buying used be aware that most electrostats and some planar magnetic speakers are likely to need the panels rebuilt every fifteen years or so. Electrostats tend not to be good choices for smoking or high dust households and almost all planars don't fare well in high UV situations such as directly in front of south or west facing windows.
Speaker manufacturers that use conventional drivers and tend to have great mid range performance IMO include Green Mountain Audio, Avalon Acoustics, Harbeth and some ProAcs. The often maligned Wilson speakers can be very good too.
Other speaker manufacturers that have a strong following but that I have not heard or not heard enough in known conditions include Vivid, YG Acoustics, VMPS, Marten, Kharma, DeVore Fidelity, Joseph Audio and some Revel and Verity Audio models.
