EdLee is trying to lead you to a conclusion, but the two of you are thinking about the board differently and that makes it difficult for you to see the lesson he's trying to gift to you. I'd love to be a bit more direct than Ed, but I'm worried about helping one side or the other ... call me paranoid, if you will.

White has 136 Points, Black has 121 Points
White has Corners AND sides. Black has Middle.

Therefore, since Corner + sides = Middle + E
Where E is a relatively small amount of points in comparison to total number of points. I can say that Middle has more territory than corners and sides (separately), obviously not together.

Therefore, my guess would be that middle is more territory, then sides, then corners. But it is either

Middle > corners > sides
OR
Middle > sides > corners

Middle > sides > corners I believe is the one that is correct.

But I am not saying that the middle is more than SIDES and CORNERS together. I am saying middle is the largest of the three.

Follow up Question: W has made 4 More moves. I was just commenting on why the board size was 19x19 and using it to demonstrate the borders of middle and side+corner. Since third line is the easiest to make territory.


<<EDIT>>
I know this whole thing depends on context of the situation, and the situation will never be as I just drew it out.

I also know that I'm probably wrong about the middle being "more" territory. It may be more actually, but I now see that the corner is "bigger" because it takes WAY less moves to secure the corner or side then it does the middle.

White has made 8 more plays.

Not at all, no problem. This whole discussion is very interesting to me because I can see the different thought processes at work!

One problem with the original phrasing of the questions was the ambiguous (and Go) usage of "big".
You're correct in your last diagram that the entire center (B's territory) had more points than the corner territory (W's).
But that's not the meaning in the question "In the opening, which is bigger -- side, corner, center ?"
Here, "big" encompasses the sense of "urgent" or "efficient". You got the correct conclusion.

Which shape are you referring to? For example, there's a broken shape in this common joseki:

Click Here To Show Diagram Code

[go]$$
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . O . . . . . . .
$$ | . . . X . . . . . .
$$ | . . O X . . . . . ,
$$ | . . O # # W . X . .
$$ | . . O W # . . . . .
$$ | . . . . . . . . . .
$$ ---------------------[/go]

The one in their game, is it joseki?