It's common amongst the average public and to a certain extent students and afictionados that are interested in military history to proclaim that iron is a superior metal to bronze, and that when people began to have the technology to create hotter furnaces that could smelt iron, it immediately replaced bronze tools and weapons, making them obsolete. The Bronze Age ended and the Iron Age began.
This is something that permeates even in circles that should supposedly know better. For instance, I still remember a 9th grade history textbook I had a long time ago (really, over ten years ago...I feel old!) that stated that a certain group of people (I can't remember which, sadly) established superiority on the battlefield because they wielded iron weapons, making their bronze-wielding opponents inferior.
In reality, this notion is as every bit as mythical as Achilles and the gods of Olympus tussling over the destruction of Troy. The end of the Bronze Age came as a result of many factors (natural disasters, the incursions of the so-called "Sea Peoples," the breakdown of old trading routes and organized bureaucratic centers of authority such as the grand palaces in Mycenae and Hattusa). The replacement of bronze with iron was not one of them. Indeed, it could partially be seen as a result of the collapse of the great Bronze Age civilizations that iron came to replace bronze.
The differences between iron and bronze simply explained.
So with these things in mind, how do they stack up against each other in a combat situation?
Unfortunately I don't currently have any equipment available to conduct a test of my own (remind me to do that someday). However one historian attempted to clash the weapons against each other and both bronze and iron weapons sustained a lot of damage.
So as you can see there was no real battlefield advantage that iron conferred over bronze. In fact, some studies and many reports (including the one cited above detailing the differences between the two metals) suggest that iron was actually inferior to the older bronze weapons. It really wasn't until the advent of steel-making (alloying iron with carbon) that the old bronze tools and weapons were truly eclipsed in quality. But that didn't occur until centuries after the transition from the Bronze to the Iron Ages. Why then, was iron adopted over bronze, as passages in the Iliad and Odyssey clearly reference, if only in passing?
I'll borrow an oft-quoted catchphrase- "it's the economy, stupid!"
Bronze, again as we know, is an alloy made of copper and tin. Copper is very abundant in the world, moreover, it is a very recyclable resource. Tin on the other hand occurs only very rarely. The closest abundant tin resources to the centers of the large Bronze Age civilizations were in Iran and Afghanistan- nearly 1,000 miles away. This required an extensive trade network that, as we know, collapsed along with the civilizations that spawned them at the end of the Bronze Age.
Iron on the other hand is very abundant and found everywhere (even more so than copper), comprising 5% of the Earth's crust. Once furnace technology improved to the point of being able to work with it, and given its abundance (plus lack of tin available to make bronze), it isn't hard to see why iron would be an attractive alternative. More weapons could be produced with more readily available resources, meaning larger, more powerful armies that were less reliant on foreign trade and thus less vulnerable- more able to secure the state.