All things being equal, size-for-size, a lightweight racing steel frame will be more flexible than a gas pipe frame, despite it being possibly over twice as strong per unit weight of material in terms of how much you can load it before structural failure occurs.
If you take material out of a steel frame by double butting, or just using thinner wall plain gauge tubes, if the outer tube diameters remain constant then you make the frame both lighter and more flexible.
I have two steel frames that are absolutely identical in both design , geometry, and size, except one is plain hi-tensile and one is butted Reynolds tubing. The butted frame is slightly lighter and rides slightly differently - subjectively more comfortable.
There are three ways you get a stiffer frame, you use more material, you use larger section tubes, or you use tube shapes that resist bending forces better. In a traditional steel road frame you can't/don't do either of the last two, which only leaves using more steel if you want more stiffness.
The thing is though, so long as the frame doesn't flex so much that the front and rear wheels run significantly out of line with each other, why would you even want the frame to be that stiff? When a frame flexes, almost all the energy it takes to flex it is merely stored, and is subsequently returned as motion when the cyclically applied force is removed. Hardly any energy is actually dissipated as heat, so there is no real efficiency benefit to making a frame stiff.