Most of those with traditional horary training/experience use Regiomantus, because Lilly used it (and so did all of Lilly's English speaking descendants) Morin de Villefranche, another major astrological-practice "reformer" of Lilly's time, also strongly advocated Regiomantus. For a few hundred years the Regiomantus format dominated European astrological practice; it was rather suddenly replaced beginning in the early 1800's (in Europe and America) by the Placidus format, which since that time has become the dominant house system in Western astrology (outside of horary practice)
Many of our traditional horary practitioners claim/believe Regiomantus is more accurate for horary than other house formats. In my opinion, this is open to question (my opinion ONLY, please!) Some important 20th century astrological authorities-Charles Carter for one-held Regiomantus (and for Carter, Placidus as well) in rather low regard, both for practical and theoretical reasons (see, for example, Carter's "Essay on the Foundations of Astrology", chapter on the question of house systems)
For me, I have been perfectly satisfied in horary results from applying the Whole Sign format (however, hardly any practitioners use Whole Sign in horary, at least in the West; Vedic (jyotish) horary-called prasna shastra or prasna tantra-only uses Equal house or Whole Sign)