What are some considerations a warrior needs to make when fighting with a bronze sword vs. fighting with an iron sword? Correct me if I'm wrong, but the bronze sword would be shorter than the iron one, while also needing to be sharpened more often and will be easier to damage or break. Bronze, however, will last longer because it doesn't corrode as much as iron (which will eventually oxidize into something unusable as a weapon if not properly cared for).
How do these factors, and others, change sword fighting between the two ages?
Comparing bronze with iron (rather than steel), there isn't much difference in quality. Both are of similar hardness (both are much softer than hardened steel), and both are reasonably tough. Bronze has a lower elastic modulus (Young's modulus), about half that of iron, so the blade needs to be a bit thicker to avoid bending too much. With bronze, this was often done with fairly thick mid-ribs, which are easy to add to bronze swords because they are cast. The density of bronze varies with the alloy; the alloys with approximately 10% tin commonly used for European Bronze Age weapons are about 10 denser than iron, so bronze swords can be shorter to keep the weight down. On the other hand, casting allows easy manufacture of blades with complex cross-sections which can be used to reduce weight.
The longer varieties of Bronze Age swords are often 60-70cm in total length (50-60cm blade lengths). These big swords are often about 650g in weight, which shows the value of weight-saving blade cross-sections (but that's a typical weight for the surviving part of the sword, without organic hilt components). It's difficult to reliably estimate a typical weight for big iron swords, since the survivors are usually in much worse condition, but perhaps a similar weight and slightly shorter average length would be normal.
64.5cm long European bronze sword: https://www.britishmuseum.org/research/collection_online/collection_object_details.aspx?objectId=808155&partId=1
69.3cm Chinese bronze sword: https://www.britishmuseum.org/research/collection_online/collection_object_details.aspx?objectId=261267&partId=1 (broken - Chinese bronze swords appear to be broken more often than European ones; they often used much higher tin contents, giving a harder but more brittle alloy)
There doesn't seem to be any big reason to expect that swordfighting changed due to switching from bronze to iron. Iron swords could be expected to be cheaper, and thus more common, at least as iron became cheaper and more common.
We don't have any useful textual sources that let us reconstruct techniques reliably. Art shows both bronze and iron swords used with shields, often being swung as cutting weapons. The long slender European bronze "rapiers" (as we call them, even though unrelated to the Renaissance rapier) may have been dedicated thrusting weapons. Very short swords may have been primarily thrusting weapons. The size, weight, and design of the particular sword would have more practical effect on how one would fight with it rather than the choice between bronze and iron.
Steel swords - especially hardened steel swords - would change things somewhat (by allowing longer blades, with sharper edges), but iron swords continued in use through the first millenium AD, and unhardened steel swords continued in Europe to the end of the Middle Ages. Thus, while perhaps inferior, iron and unhardened steel swords were considered usefully functional quite late.
For a nice paper on Bronze Age swords and swordsmen, see Molloy, B. (2010), "Swords and Swordsmanship in the Aegean Bronze Age", American Journal of Archaeology, 114(3), 403-428. http://www.jstor.org/stable/25684288