it's more likely the down tube to bb that is going to flex. if you rode a skinny steel hardtail with qr forks, square taper bb and cranks back to back with a known stiff alloy frame (like a SC chameleon) with modern external bb cranks, tapered steerer, bolt through forks and oversize bars
you would notice the difference even if the tyres were identical.
it's more likely the down tube to bb that is going to flex. if you rode a skinny steel hardtail with qr forks, square taper bb and cranks back to back with a known stiff alloy frame (like a SC chameleon) with modern external bb cranks, tapered steerer, bolt through forks and oversize bars
you would notice the difference even if the tyres were identical.