Maybe I'm a bit too late to weigh in on this, but after reading pcmacd's refution of my claim, I felt the need to defend myself and my training. I'll stand by my original statement that carbon steel is generally stiffer then stainless.
For us engineering types, let's open our ASM handbooks to volume 1 ( or in my case Callister Engineering Materials and Science: an Introduction 5th ed. to appendix B, which copies and references the pertinent ASM values) and we find that plain carbon steels have a listed modulus of elasticity (or Young's modulus if you want to get confusing) of 30e6 or 30 million psi.
Of the listed values for martensitic stainless steels, grade AISI 410 (commonly used in gun barrels, although others may be used) is found to have a published modulus of 29 million psi.
Similar, yes. Identical, no. While the Poison's ratio for all ferretic alloys is assumed to be the same at 0.30, I distinctly remembered that stainless steels were less elastic then plain carbon steels. It turns out that AISI 410 is at the stiff end of stainless alloys. They tend to go downwards from there, ending in the range of 28e6 psi.