As a player, any of these options can be great, the dependency is on the GM. If the GM isn't feeling the game, no one will enjoy it and/or it will die an early death.
However, if I had to pick an option as a GM, I think I prefer Adventure Path with Sandbox elements.
I should state, that in almost every game I have ever run, I created a world and an overarching storyline, but let the players decide how they wanted to interact with said storyline. Ignoring the plot may not affect the player characters' immediate situation, but eventually there would be a breaking point where ignoring the plot would not be feasible.
This allows me to make the world feel lived in, as NPCs and locations have to deal with the fallout of the plot even if the players choose to go in another direction. As a GM this keeps me engaged with the world as much as I am engaged with the player characters.