In any non-linear game, I want to have the utmost control over who I'm playing and how they're leveled. That being said, it boils down to the instrinsic gameplay qualities of the title. If the story is fundamental to the player's progression, like in Metal Gear, then a pre-developed character with customization options can make a linear character design feel free-flowing. On the other hand, if the game's story comes secondary to gameplay, like in World of Warcraft, then building your character from the ground up is ideal. And naturally there are instances where the rules work oppositely... Fallout 1 and 2 have highly detailed stories, but the player is free to create their own characters and micro-manage stats. Grand Theft Auto is an entirely non-linear franchise of games where story is secondary to the quality of gameplay, but you're given a static character to explore with.
At the end of the day, I think it boils down to your own wants as a game designer. From a development perspective, would a custom character system integrate easily, and if not, what challenges would it present? Can you deliver the game's story through a custom character or is that character central to the events of the day?
And that's another good point worth mentioning... does the story revolve around the player's character? Are they superfluous in the grand scheme of things, an unpredicted wild card tossed into the deck through some hapenstance, or are they key to the start and end of the story? In other words, was the player thrust into the events of the day, or did the events of the day come into existence purely because the character did or said something? If the player's role is central to both the cause and the effect of the story, you might consider going with a static character with customizable options, whereas if this isn't the case, I say grant the player freedom in developing their character, bolstering your project's suspension of disbelief by thrusting the player into the game as themselves, rather than assuming the role of someone else.