Or rather, the Sony and others that use Dolby headphone use HRTF to downmix audio. The JVC and Smyth use impulse responses and correlation to downmix. The latter are better for getting how it should sound, provided the impulse responses are captured properly. The latter is popular because they can capture ambience so how a real room sounds.
HRTF methods use a mathematical model of how sound performs and offer an idealized simulation of a perfect room.
So far, the big differences are that the JVC uses it's own headphones and a fixed impulse response, while the Smyth is more flexible and allows using your own headphones, applying headphone correction curves similar to room correction, can handle head rotation (so a sound coming from the left will now come from the front if you turn your head left), and making and applying custom responses so your audio can sound how it was measured.