I'm with 9:19, I prefer when the protagonist has a strong personality. I don't play VNs as myself, that is what my life it for. I prefer to step into the shoes of another and see what their life is like, to do and be things I can never be. Even when playing more open ended RPGs such as Skyrim, I create a character who would make sense in the world and follow the story that is created. I think it is normal to have a number of options even playing as a designed character. I mean,
we don't always act the same way all the time. We constantly make choices in our lives, why wouldn't you expect the same of a character? The exception to this are the more open ended RPGs were you can make heaps of choices, but I do think the story and characters can suffer a bit from this and there can be a disconnection between your actions, the reason you choose them and the result. Case in point is in ME3
I choose not to inform the Krogan about the Salarian sabotage, I told Mordin directly. This was because I didn't want to strain the relationship between the Krogan and the Salarian over something that happened hundreds of years ago and something I could fix quitely. It hadn't gone well with the Turians and I didn't want to add another one to the pile that was already pissing the Krogan off. However, the game informed me I made these choices because I didn't trust the Krogan.
At least with a predefined character you can inform the player about who they are playing so that the choices after that will make sense from that point of view. People are good at empathy, I think it works well with getting people to see things from a different perspective.
So I'm fine with a range of characters, as long as they are unique. I do have a soft spot for strong female characters though.