Peri's mostly got it, but it depends alot on what type of iron and what type of bronze you're talking about. Properly worked bronze is about as "good" as decently worked high-carbon iron (we'll call it quasi-steel). Cast bronze (more common in the Bronze Age) is not quite as good as cast iron. Both will hold a nice edge, but the bronze will shatter more easily than the iron, assuming you apply equal force to both.
In game terms, I think it's fairly safe to assume bronze is well worked, wheras the iron has little to no carbon content that doesn't occur naturally - that's what in game steel is. So, in that sense, the bronze should actually be superior to the iron.
Historically, the big shift from bronze to iron happened because of logistics. You need copper and tin to make bronze, and it's a little more labour intensive, wheras you just need iron to have iron, not because the iron available was "better". When different methods of introducing carbon (also plentiful) into the iron came around, iron and steel became both less labour intensive and resource dependent than bronze, as well as "better" for pretty much any application.