Some games give us certain protagonists that are already set in a certain image, think Mario, Link, Nathan Drake; but some games give us a chance to customize a character in our likeness. We can change their name, their build, their clothes, basically build them from scratch. A question I have always wondered while I made "Character X" is do others, including myself, make the character to represent myself or how I think I am? The majority answer you would hear if you asked this question is to any gamer would be they modeled the character after themselves...but how much of that is true? I know my older brother always looks for features that are most similar to him and then adds things he always perceives as cool for the character. A counter to the argument of building a character in your likeness is this is a fantasy, so you can make the character in anyway you like.
But that's not necessarily the point I am bringing up, I am saying when you build a character in your likeness, is it a true representation of the person you think you are? Sometimes you may make your character and you think it totally matches you or your inner-persona, but when showed to relatives or friends they go "who's that supposed to be?" I guess the basic point being brought up is how honest are you with yourself when creating the character you think of as yourself.
In my opinion and as lame as it sounds, I am on the side of giving us character's with set images, persona's, etc. because, not that I am lazy, but I think it gives the game feel a more lasting experience. Some may argue that Fable is a fantastic game, and I cannot deny that, but I have always felt it is more memorable for a game to have a cast of it's character's already there for us. By having built characters, you can find likeness' from you and the character, you can grow to love or hate them, heck you can even be inspired by them; compared to the point of building your own character where there is less feeling of attachment (where it should be the opposite!) Most times when I create a character on my own it feels almost like a forced concept; yes I want to look cool and I love it the first day, but after a while the hype for said feature dies down.
Not necessarily in all games (think like Halo, where you unlock cool armor to showoff to friends with), but in a majority yes. I will never forget character's like Zidane Tribal (FFIX), Nathan Drake, Sonic the Hedgehog, even Banjo-Kazooie because they are all character's I really love and have great experiences with; be it not only gameplay, but one-liner's, or just their cool attitudes.
Do you like creating characters or are you like me and want character's already made so then you can find your relationship with each? Does the game matter for the character?