Whereas the Catholic priest seeks the salvation of the penitent (and secondarily his reconciliation with the Body of Christ), the Solarian cleric uses his knowledge of actual sins primarily to improve secular society.
Without overly stretching the point about the "Italian" quality of the Solarian notion of sin, it is true that this attitude resembles Dante's Inferno, where the more serious social sins are judged worse (nearer the bottom of Hell) than private ones, such as lust (nearer the top).
But the most significant difference between Trent and Campanella is that the Solarian priests do not form a separate group.
Furthermore, the regulations on confession are few and simple (as are all Solarian laws); Trent canons on confession filled tomes.
And as if that weren't task enough, Honor must also face down a centuries-old nemesis in the crumbling, but still mighty, Solarian