You speak of them as though they were mutually exclusive, as if superior stats somehow made the player dumber or more incompetent in some manner.
Given all other things equal, if we assume that 2 PCs are played with just as much skill and finesse, the one with better stats would always be better off. So I don't see why I deliberately need to gimp my own PC just to prove a point?
They're not mutually exclusive. Since it's the skill of the player that matters, you certainly can play a character with all 18's with just as much skill and finesse as a character with average scores. It is not incumbent upon a player to play a noodle-armed, butter-fingered, asthmatic, mentally and socially inept character to "prove" that you are a skilled roleplayer. (Besides which, I play D&D for fun, not to prove points.) If the game is fun I'll give it a shot.
I've had just as much fun playing a character made using 2E's method I (3d6 in order) as I have in a game that used a 40-point point buy. I really think that having high ability scores isn't as important as some claim it to be. But then again, character power (and not even necessarily success) doesn't equate to fun for me.
Personally, I find it more challenging and less fun to play characters with little differentiation in ability scores because nothing stands out about that character's natural talents. Whether the character is hopelessly average (all 10-12) or superheroic (all 15+),
nothing stands out. The choice of character class doesn't seem as natural and it stretches my suspension of disbelief to have a character that could be good at anything he wanted to try. I like having a few shortcomings when I play. Characters that can do just about anything on their own need others less, which detracts from the dynamic of a balanced adventuring party.
This is all beside the fact that ability scores really don't have much to do with the root causes of most failures for characters and their parties: bad dice rolling, poor player skill, and poor DM skill. You can have all the positive modifiers in the world and it probably won't help too much if you keep rolling 1's all night long. Conversely, even a wizard can become a melee terror if the player is rolling 20's all night and the DM keeps rolling 1's for the monsters. Nothing about your character's ability scores can (nor should) keep a player from making bad decisions, like sticking the character's head into the darkness inside the mouth of the carved green devil-face in the Tomb of Horrors. If the challenges are too hard for the characters, they are too hard
because the DM made them them too hard, not because of the ability score generation method or any other mathematical function of the game.