There is a very real correlation between size and strength,
in any one particular lifter! If you say, "so and so is much smaller than me yet can lift more", then you haven't thought things through.
And if someone says he doesn't think strength and size go hand in hand then he isn't being honest, or hasn't thought things through.
Every bodybuilder takes strength increase as a sign of growth and progress. Say you go in and do 30 reps on the leg extension with 150lbs to failure yet last workout you did 180lbs for the same amount of reps, do you take that as a positive or negative sign? Negative of course. But if you do 200lbs for 30 you know you are doing something right. Right?!
Those westsiders "squatting" huge weights have big guts, big glutes, big erectors,
because that's the muscles they use in the lift! They have small quads because they are hardly used. Many pro bodybuilders would kill those guys on Olympic squats or hack-squats. And guess what, the bbers have bigger quads.

It's scientifically proven that the cross-sectional area of a muscle is directly related to it's strength. I don't even know why this is debated. Well I do know actually, it's because of misunderstanding the terms in the discussion. People don't understand what the other really means.
An personal example. Bodybuilder I train often squats with a powerlifter. Powerlifter max squats 300lbs more than the bb, in a suit. Even if bb puts on the suit the PLer would still squat 300lbs more since the bb doesn't know how to use the suit. Bodybuilder kills the PLer on narrow stance Olympic squats without gear. Guess who has bigger quads?
Powerlifting involves a lot more than muscular strength. Mainly technique and "angles" due to structure. Doesn't change the fact that a bigger muscle is a stronger muscle
all other factors being the same.