The balance of freedom and structure in a mentorship style

[NewScientist12]

I tend to approach research from a creative, big picture side of things, but, at the same time I also can often get lost in my own big ideas. From anyone's experience as an undergrad or grad, do you think I'd fare better in a more structured environment or one that affords me opportunities for free exploration? In graduate school it's obviously a balancing act, but if you were (or are) in my shoes, what would you do? I have two great offers, one to work with a mentor who is more structured, and the other who takes a relatively "hands-off," almost even lax approach. 2 weeks to make some big decisions... any input would be appreciated.