In this article, Josh Bycer give some example on how it's crucial to really care about choice liberty we give to the player and how they can (really) badly affect player experience if it's actually unbalanced.

It's a really good though because I think that giving choice in design is one of the best way to really get the opportunity to exploit video games as an experience medium (I remember Sid Meier saying something like "Giving the player the opportunity to chose open the door of "What if I had choose the other option"... and we he is engaged"). But, use it carefully as it's not THE safe solution to good game design :)