Thank you! I've been wanting to start this thread for a while now. Honestly, the only things that matter here are realism and believability. Information can be bad if it is realistically unavailable to your character. Those arguing otherwise may as well permanently lift the fog of war and automatically know of every plot attempted in the game. Simply put, anything which gives the player immersion and makes him behave like a true medieval lord is good while anything which continues to make him feel/behave like a guy playing a game is unacceptable. Knowing everything about a character thousands of miles away displayed as a simplistic number system clearly falls into the latter category.
What is realstic is reputation. People have reputations to give others an idea of what they're good and bad at, and secrets, such as certain genetic traits. There is no question that, in the name of believability, stats need to be replaced with sentences covering a small range of numbers. If you're not particularly bright, what would you expect people to say: "He's a bit slow," or "he's clearly got an intelligence level of 3?"
Traits ought also to be more hidden, considered on a one-by-one basis. There's no way to hide your lisp from those around you, so it should be displayed for the world to see - it's a part of your reputation. You're known as a great theologian, so this trait would naturally be made visible, but quite a lot of personal traits, particularly things like deadly sins or homosexuality which could be practiced in secret, should only become available for all to see if caught doing something and unable to stop the rumours.
There is only one number I can think off-hand which should always be available to the player: His own treasury, and perhaps even that should be approximated unless he has the "greedy" trait and is always counting it.