In Reborn, I'm just a guy who's there, to do these events, drive the plot along, become a hero. I feel somewhat Disconnected to the Region.
In Rejuvenation, Even if the Character is the Classic Silent Protagonist (Like Link, Every Pokemon Protagonist in most Pokemon Games, The MC in South Park: The Stick of Truth), there still is a sense of Mystery to this Protagonist. I want to know His/Her's role in the prophecy. Is my Mother even my Real Mother?
Also, Desolation, In my opinion, does this best. It doesn't really create a sense of mystery about the Protagonist, or make you the subject of a prophecy, but it does give you several choices that drastically affect the Storyline. You know when a choice is gonna matter later, such as giving a stone to either Shiv or Nova. The Fact that you have some degree of control over what happens creates that sense of a connection to the game, and the region.