No, they are completely different. Stiffness is related to the slope of the stress/strain relationship (elastic modulus) in its linear range. Strength is how high the curve goes before failure. Not the same at all. A material can be very stiff (glass), yet not strong (glass with a small surface crack). A material can be very strong (spring steel), yet not very stiff (spring steel).
Let's say you support the empty pipe as you say above (as a simply supported beam) and measure its deflection in the center. Now stand the pipe up, fill it with concrete and let it cure and then support it the same way again and measure the deflection in the center. Which case do you think will have greater deflection? And now explain why your stiffer pipe has more deflection than the less stiff pipe that has no concrete.