Isn't it like The Divine Comedy where King Minos is the Judge of the Dead but is only in charge of telling people where they belong while Hectia seems to be more in line with the same position as Satan just without being trapped in the ice. Perhaps if this is more an amalgamation of different religions then because she is a greek figure as the sisters of fate in one body they probably share the same position of authority. I remember reading that Shiki is the Judge of hell for Oni or something so she could potentially be a superior.
ZUN: As for that, I had wanted to bring a character from Hell into the story. A Hell different from the one underground. Though she's different from oni, she's just a normal goddess of Hell. In terms of status she's absolutely higher than Eiki. Eiki's a judge, but she's a part of a society of oni. However, Hell isn't limited to just oni. There are plenty of things we haven't seen yet in regards to Hell. And it would be easy to make new worlds if they wanted to. An infinite number of worlds can be made. All those mysterious aspects can be considered Hecatia's "Otherworlds".
Basically, Hecatia's Hells are different from the Hell full of Oni where Shiki sends people after death. Also, Shiki is just a judge for the dead of Gensokyo in a society of Oni, not some big boss of Hell, while Hecatia "controls" the Hells of the Moon and the Earth, which includes both Gensokyo and the Outside World. On the other hand, Hecatia isn't really like Satan because the wording (just a normal goddess of Hell) implies there are others gods of Hell around, which i suppose might be gods of Hell from other mythologies.
I wonder if Satan himself (herself) is part of this at all, since christian mythology doesn't seem to have much spiritual meaning in Touhou.