Multiple viewpoints

No particular problems (haven’t started writing yet), just wanted to pick up opinion on a multiple-viewpoint game.
Scenario: four main characters who have to solve individual puzzles in order for the game to reach its conclusion. It’s a 1950s girl gang whose leader is in reformatory, and the object is to break her out.
Should I shift the viewpoint based on time, number of moves, whatever? Should I let the player control when the shifts happen?

The two common strategies here are “player controls viewpoint” or “shift viewpoint every time a scene (puzzle) is completed.” The latter means you have to plan out a sequence of puzzles, of course. The former gives the player much more control over the general order of events.

(This is more of a “General Design Discussion” question.)