I personally believe that character skill should be the overall determining factor though I wouldn't mind if player skill was taken into account by some degree.

For example, the combat system. As Kovacius mentioned in a wonderful post Mount & Blade had an almost-perfect blend of player skill and character skill in its combat system. Factors such as blocking and timing attacks are all heavily dependent on player skill, but it is the character's effectiveness that determines the overall outcome. You could argue that TES does the same thing but MB, in my opinion, had a more refined system that was both exciting and RP-ish (is that even a word?)

I think they need to matter just as much as character skill. Games that only have character skill no longer engage me.