Even iron, before tempering, is merely somewhat better than that of appropriately tempered bronze. Tempering alters the crystaline structures of metals, which allows the alteration of material properties; thusly, if you want to be super realistic about it, mithril probably would not be able to be much better than well tempered iron.
Neither iron nor bronze can be "tempered" proper, though they can be work-hardened/beaten/cold-wrought/etc. Given equal amounts of work-hardening, wrought iron is about 20%
weaker than bronze. The shift from bronze to iron was economic, not structural. Iron is way cheaper and more common, and iron production with local ores isn't dependent on trade (copper and tin ores occur in close proximity in only 1 or 2 places on earth).
Also, the "tempering" difference really isn't true either. Not every metal in the world is steel. Copper, bronze, wrought iron, etc., can be made about 2x as strong and 2-2.5x as hard, via work-hardening. Cobalt and tungsten alloys can also only be work-hardened for about the same proportional increases, though they can rival steel once so hardened.
The strongest titanium and beryllium copper alloys don't work-harden well, but can be cryogenically aged, for about a 25-50% increase in strength and a 25-50% increase in hardness (some titanium alloys can be heat treated and quenched a bit like steel, but only for about a 25% gain in strength and hardness, and the heat treatable ti alloys are also weaker than the cryo-aging ones). Not very much of an increase, but they once again rival steel once hardened. That also means, obviously, that they're extremely freaking strong before hardening, making them very difficult to work with.
Steel can be made about 8-10x as strong and 5x as hard without being brittle (if being brittle is okay, then you can go 20x as strong and 10x as hard), via heat treating and tempering. It's pretty unique in that respect.
Then the fancy amorphous alloys, you can't harden or strengthen at all. But you can't really weaken them either, like by repeated bending.
So if you
really want to be super realistic about it, you need to first decide if mithril should be treated like a "normal metal" (the first category), an alpha/beta alloy (the 2nd), a crazy phaze alloy (steel), or an amorphous alloy.
Things which apply to one category do not necessarily apply to others, despite what people with a fancy education in a completely unrelated topic might tell you.