Hmm, honestly a pre-determined character would be much easier for you as the author, I think. Though, I think there is a sort of 'middle ground'. What I've done with a game I'm working on is a pre-determined main character, but the player's choices throughout the game trigger different variable scores to go up and down. I call them Behavior variables.
Basically, depending on the choices the player makes, the variable scores will trigger certain options(or scenes) to appear/disappear giving the character a more personalized feel to him.
That's how I tackled it. But, you have to keep careful track of what score the player is capable of having per variable up to the point where you create different paths that will appear or be hidden based on scoring. When I first started I accidentally put impossible scores in the link restrictions and it was impossible to get any of the paths until I realized it and calculated the possible scores.
There may be scripts that are much easier than what I just described. I know practically nothing about scripting :(
As for what I personally prefer, it depends on the story. Certain games suit pre-determined characters and vice versa. It all depends on the authors approach. :)