There's no single rule: every piece of equipment has its own configuration. That said, I cannot think of any case where an attribute change by anything but +10% per quality level, so a quality 6 has +50% over the base attribute of a quality 1. Mind you, everything above primitive tools has random stats which go from -15% to +15%, so a +15% quality one could have the same stats as a -15% quality 4.
But tier 0, 1, 2, and 3? That's balanced by hand without any clear rules as far as I can tell. In fact, it's a pet peeve of mine that the iron spear adds almost nothing to the stone spear, whereas, on the opposite end of the spectrum, each tier of the sledgehammer has a huge jump in stats.
And to confuse things even more, not all attributes change, and the stone axe has no equivalent at any other tier.
Assuming you know how to build forges to handle iron. And, on top of that, forges to handle steel. Another issue with iron is obtaining it, but I don't think we have to worry about that on a post-apocalyptic society, unless radiation is an issue (in which case, yeah, iron sucks). But, hey, most post-apocalyptic games assume there's scarcity in a world where less than 1% of the population has survived, which would just not be the case.