Oh God. Researching the answer took a long time. Thank God for Google.
Ok. The tensile strength of plain copper is 200 Mega Pascals. What the heck is a Mega Pascal? Let's convert it to Freedom Units. 29,000 pounds per square inch. That's more like it.
Now. The low-end bronze alloys have a tensile strength of 310 Mega Pascals or 45,000 pounds per square inch.
That's why the Phoenicians took the trouble to sail to Wales and Cornwall from Lebanon to trade for tin before the Iron Age.
Caravans also traveled from mines in Afghanistan.
Pure iron has the tensile strength of 275MPa or 40k psi. Not much of an advantage. But when the Iberians invented case hardening (carburizing the surface layer of an iron object), then heat treatment (quenching and tempering) c.900 BC. It went up to 490 MPa or 71k psi.
The problem with iron is one blacksmith can only forge one sword. Two bronzesmiths could cast 6 or 8 bronze swords via the lost wax process. They made a few wax models of the swords. And stuck them together in a “tree".
Copper, Brass & Bronze are work hardened. That means hammering them. Heating and cooling them is to anneal them. Making the metal pliable again. I don't think these metals trap carbon atoms like iron, tungsten or titanium does.
Update:
Recently I read an archaeological article where they catalogued Egyptian & Hittite iron artifacts in museums & collections. It turned out that the Hittites who were believed to be pioneers in iron making, weren't in reality. There were as many Egyptian iron artifacts as Hittite ones. They were all made of meteoric iron. The first culture to mass produce iron by smelting ores were the Etruscans c.800 BC to 390 BC. They left so much iron slag, Mussolini processed them into steel in WW2.
Update:
Bronze Age swords bear the marks of skilled fighters - HeritageDaily - Archaeology News
Wootz steel was the space age material of the Ancient World