So this question asks whether or not it is accurate that bronze armor is stronger that iron armor in the game and in the real world. At first I figured Less' answer was good enough because everything he said was correct, specifically
Early wrought iron wasn't better. Unfortunately he really failed to explain why
Early wrought iron was better. I don't mean more abundant, or easier to use, I actually mean harder.
For those of you who don't have the time to understand basic metallurgy I'm going to explain how Iron was used during the Iron Age, why it was stronger than Bronze and debunk the myth that the WTC was a conspiracy by the US government, but that last one is incidental.
Back when I took Solid State Chemistry at Northwestern, they made us memorize the Iron rich end of the Iron/Carbon phase diagram. I've reproduce it for you here so I can make reference to it:
Historically, Steel dates back to the 4th Century BC (though there have been archeological finds as early as 4000BC). Both the Roman Military and the Chinese of the Han dynasty used steel as a source to make weapons out of, though through very different techniques. When we historically refer to the Iron Age, we're referring to a period where Iron was used in industry, however, the specific usage was as Steel. Though we separate this from the usage of Steel in the 17th century onwards, because the Steel made during the Iron age was largely Iron wrapped in a few Micrometers of Steel.
To create steel you need two components: Iron and Carbon. Iron bonds with the carbon to create Fe3C, or Cementite. This is sometimes referred to as Beta phase Iron, where as Fe separated from C is usually referred to as Ferrite or Alpha Phase. Above 727°C Ferrite changes its crystalline structure from body-centred cubic to the face-centred cubic thus losing 70% of its strength. This is the reason that we heat Iron to work it into shape and the reason that the burning of wood or jet engine fuel (while not normally hot enough to melt Iron) can cause a massive Steel supported structure to collapse. This is usually called Austenite or Gamma Phase.
If Iron is heated with wood (or other Carbon burning heat source) some percentage of that carbon will make its way into the Iron. As heated Iron shifts from Alpha to Gamma phase, the change to face-centered cubic allows for carbon to be dissolved into the lattice structure of the Austenite. If you were to then rapidly cool the Iron (a process known as Quench Hardening), the result is a mixture of Alpha and Beta phases. At ideal mixtures of Carbon and Iron this is known as Pearlite, or more commonly Steel.
While Ancient Iron workers didn't understand the chemistry that they were performing the result is that the Carbon from their forges was combining with the Iron to form Steel. Thus the inaccurately named Iron age was in fact a Steel age. However, the penetration of the Carbon was very low (a few micrometers) so a number of different civilizations sought specialized techniques to increase this penetration (not that they understood what it was they were doing). Crucible steel, berganesque steel, even the folding techniques of Ancient Japanese sword smiths were all examples of attempting to achieve better penetration. It wouldn't be until the 17th century that Modern Steel was achieved.
When Toady redesigned the combat system in DF2010 (the successor to 40d), he changed it from a heuristic system (with values he decided on) to a system based on the properties of Yield, Fracture and Elasticity. He did this in an attempt to simulate proper Stress/Strain equations. However, because Iron has poorer properties in comparison to Bronze, the result was the Iron Weapons/Armor are inferior to Bronze Weapons/Armor in DF2010. However if you actually look over that chart you still notice that in some cases, Iron heavily out performs Bronze. I'd say there is no rule of thumb for when one is better than the other.
TL;DR Historically, Iron has been stronger than Bronze because of the presence of Steel in the Iron due to the processes by which it was made. Steel also losing 70% of its strength at temperatures over 727°C; so jet engine fuel could be the cause of the collapse of the Steel supports in the World Trade Center on 9/11.
Though the latter is not definitive.
While there were definitely versions of dwarf fortress wherein bronze was unquestionably superior to iron, weapons testing in 31.12 has proven this to be false. Iron is now the third best material for armor, though it is pretty much equivalent to bronze when used in weapons.
I cite this thread: http://www.bay12forums.com/smf/index.php?topic=53571.0 which contains the relevant data (and already tabulated, too!).
So garb your dwarves in iron!
Yes, this is absolutely accurate, in the real world. The reason that Iron overtook Bronze as the primary metal in arms and armor historically had more to do with scarcity and cost than quality. Early wrought iron wasn't better, it was just more common and 'good enough'.
Raven Dreamers answer however, indicates that it is in fact no longer true in game.