Hmmm.. I'd never really thought about putting Girl Genius and ancient mythology in the same frame of reference. Eek. But, okay.
There are parallels..
When Osiris came to power, he stopped the Egyptian people from fighting among themselves, gave them laws, civilization and peace. In GG, the current lack of war is called "The Baron's Peace"
Klaus did "die"; I assume from his scars and the construct patchjob. That would technically mean that Gil, like Horus, was conceived post mortem.
Osiris was dismembered and reassembled, and Klaus certainly looks like that was what happened to him.
There is the ongoing storyline with Klaus perhaps being dead/missing..(I really hope Not Dead..) ..and the way that Gil and Agatha are beginning eclipse their parents for Spark and abilities. Horus did eventually replace/overshadow Osiris.
Also, Horus' surviving parent had to hide him as a child, to protect his life, as his uncle wanted him dead. (Gil and maybe Skifander?)
I'm sure someone with more experience about mythical archetypes could do a much better job with the subject. And maybe not sound pretentious somehow.
It's been a long time since I read Egyptian mythology and even longer since I read Hero with a Thousand Faces.
-mutters- ..too busy reading Girl Genius ^.^