Aluminum bicycle frames are almost always greatly stiffer than steel. They need to be, because aluminum suffers fatigue (stress cracking from repeated bending) much easier than steel does. This is why aluminum bike frames almost always have fatter tubes than steel bike frames do.
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The problem with overloading or modifying a bike frame made of aluminum is that aluminum alloys owe a lot of their stiffness to the final heat-treating applied, where they are heated up to ~1000F and then cooled very slowly in an oven. If an aluminum frame cracks, the heat involved in brazing or welding it (with any welding method you use) is hot enough to also ruin the heat-treating around the repaired area, making it even less stiff than before. So to fix any aluminum bicycle frame, you need to weld it up, and then have the whole frame re-heat-treated. There's no other way to do it right.
Steel (non-stainless) is the better choice if you want to modify the frame, build a frame from scratch or want to fix it yourself if it cracks. The fatigue resistance is higher than aluminum. It can be brass-brazed with a cheap MAPP/propylene torch. The names "mild steel", "hi-tensile" and "cro-mo" don't really mean much since they don't tell you the particular alloy. Mild steel is cheap but is softer than typical structural-grade steels.
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If you are buying steel tubing for a bike frame (in the USA) and don't know what kind of steel to get, ask for 4130 steel. This will be thin-wall, extruded, seamless, "cromoly", structural-grade tubing that works well with all welding methods. It's what you want.
If you ever happen to find a stainless-steel bicycle frame (one that is unpainted yet has no rust, and that a magnet sticks to at least a little bit) don't do anything to it until you identify it. Don't even rub it with steel wool or scotchbrite to "clean" it, because you can scuff the surface finish that way. Stainless-steel bicycle frames from ANY time period are rare and pretty much all of them are collectible,,,,, $$$.
Titanium is nifty and all, but it costs about 10X what typical steel or aluminum does and it must be TIG welded. As far as bicycles go--titanium parts are light, but also very flexy in use. Titanium has a very high fatigue resistance, and so to make the parts lighter, they are made very thin on purpose to save weight.