Pretty sure Jyggalag is just another kind of insanity; Obsessive Compulsive, pathological control and neat freaks, etc.
Sheogorath/Jyggalag...when (s)he switches, (s)he doesn't become sane, Jyggalag is as hokerrs as Sheogorath, just in a different way.
No, Sheogorath is the complete opposite of Jyggalag. Sheogorath is the Daedric Prince of Madness, while Jyggalag is the Daedric Prince of Order
There seems to be indication that Peryite is gaining prominence, and it wouldn't be surprising if he had somehow absorbed or conquered Jyg's domain.
Jyggalag's domain was Shivering Isles. After he was defeated, he simply left, and his fate is unknown. Most probably he wanders around in Oblivion or make a new Realm of his own, as Sheogorath is still alive and well (meaning he still has Shivering Isles in his grasp)
Also, Peryite's order is a bit different with Jyggalag's. Peryite's "order" is more like "nothing wrong is happening", while Jyggalag's is more like "every command is carried out without error"
If anything, Peryite is also known as "Taskmaster". And "Taskmaster" is pretty low in chain of command tree