It kind of depends. My group is all new to the system (as am I, as is everyone, I guess, since DFRPG is new. But we have no prior FATE experience, either), and writing up characters is a great way to learn. So we're set to have sessions where they will draw up NPCs - lovers, enemies, informants, everything. So they'll know the stats for those npcs, which will be on google docs.
They know all of the aspects for the city, and themes and threats. But, they know about the white court presence (one of the theme faces), with no stats. So they don't know for sure that the Duke isn't also a sorcerer, ect.
Generally, if it's an ally, i share stats. If it's a bad guy, they know if it is a face or something, but no stats... i actually keep blank sheets and write in stats as they discover them. Once the guy dies or is rendered moot, i share stats.
because we're playing up the detective angle of DF, i kind of can't tip my hand without ruining a mystery.
Still, in the last battle (w/ a -19 refresh necromancer and his two -6 sidekicks) i openly had their sheets exposed so we could show how damage is tracked, ect.