The Just City is about time-travellers attempting to set up a society modelled along the lines of Plato's Republic by taking children whose destiny otherwise would have been slavery to a purpos-built city on Thera before the explosion. This is a world where the Greek gods (and others) exist, and one of the viewpoint characters is a secretly incarnate Apollo. The basic concept is of course brilliant, and I think this is the most detailed version I've seen of it. The grand plan is disturbed by many things, including the gadfly questions of Socrates, and the rise of the city's robots, from off their knees, disturbing the narrative in a manner very slightly reminiscent of the Mule's disruption of Seldon's Plan. The intellectual problem and the emotional arcs of the main characters - particularly the very tricky case of Apollo - are very nicely done, and the denouement is satisfying while also creating space for the sequel.
I enjoyed The Philosopher Kings as well, but not quite as much. There's a great riff on the adaptation of Christianity to a Platonic society, mirroring the adaptation of Plato to Christianity in our timeline; the ending is also a good conclusion for both books. But we lose a favourite character at the beginning of the book, and another engages in a pretty horrific act in the middle of the story (though in fairness it is well-rooted in mythology); also the whole plot is based on the notion that the traumatic events of the end of the first book would have resulted in a complete loss of contact between some key characters for two decades, which given the geography seemed improbable to me.
So I think The Just City is likely to make my Hugo list, but The Philosopher Kings is not; however I still recommend them both.