It depends on your goal, too. I was involved in an entirely improvised short film, but it was shot mockumentary style, so it was more the case of a single character improvising some scenes, but mostly sit-down interviews in the typical documentary style. For that, we had a few questions in mind to ask the character, but nowhere in particular to go with the dialogue. Shooting a lot of different questions and answers and b-roll, and then creating the story in editing was the production flow.
With a narrative, if you have to tell a story, entirely improvised, you're probably better off with a solid outline of beats you need to hit, points that have to emerge, knowing where Point A is and how you're going to get from there to Point B, C, and so on. Giving the actors lots of direction in terms of what their character's goals and motivations and history are would help them make the right decisions for their characters. And you would probably be more reliant on how a certain take goes (like, if you get certain plot points out, naturally, in a take, you might not want to inter-cut between different takes), so shooting two angles at the same time, giving you the option to cut between cameras, might not be a bad setup.
gelder