What you're seeing re:springback is the proof. The amount of springback is proportional to the strength of the steel if the sections are the same.

Every kind of steel has the same or nearly the same Young's modulus or modulus of elasticity, or spring rate. This data is available.

That's the elastic region. The slope of the stress vs. strain curve is the same up to the yield point, but where the mild steel curve flattens out (yields), the higher strength steel continues upwards and flattens out (yields) at a much higher stress. So you have to put much more stress on the CrMo steel to get it to permanently deform (bend or yield) than you do with the mild steel. When you take off the load, the steel runs backwards down the curve, and because you have to stress CrMo more, it has more distance to return (springback).

The CrMo chassis is NOT stiffer than a mild steel chassis, all things being equal, because of the similarities in spring rate. Also the section of the mild steel tube is much larger so it will be stiffer up to the point of yield.

Strength is very much different. Strength means how far you can bend something or twist, before it permanently deforms. In this the Cr-Mo wins.

Assume a chassis made of the two materials, but equal in diameter and wall thickness.
In a crash, a certain amount of energy is working on the frame trying to deform it. The mild steel will distort and then yield as the yield point is reached. The CrMo will distort and take a lot more energy to get to the point where it finally yields or buckles.

So to offset the lower strength of the mild steel, the sanctioning body mandates larger diameter thicker wall. That should give the same resistance to permanent deformation between the two. In this case, the mild steel will deform less until it fails. The CrMo will deform more before it fails. If the sanctioning body's calculations are correct, they will both permanently deform at the same amount of energy, just behave in a different way as they get to that point.

My thanks to Prof.Ronald Apanian for teaching me how to understand this.

R.