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@Oswald
Strength is a measure of the ability of the material to withstand failure and stiffness is a measure of the ability of the material to resist deformation. So to use an analogy an elastic band is high strength low stiffness .. The ability to resist bending forces is a function of the second moment of area of the material.
So for two round tubes of the same external diameter made of different carbon steels with different wall thickness the higher grade steel (thin walled material) will flex more. Which is what Chris Juden's is describing in the last paragraph.
If you increase the diameter of the tube you increase the second moment of area and increase it's resistance to bending. So the thin walled tube will now flex the same amount as the thick walled smaller diameter tube. But it will weigh less. That's all theoretical ..