It's definitely a lot more fun if you don't watch each others moves, especially during negotiations so the other doesn't know what you have.
On the other hand, the player that gets all the popup information on his turn (like so and so is building a wonder), should inform the other, including when each of you has started to build a wonder. Of course, this is up to you, but it is information you would normally have in an SP game.
Cheers,
CK