I don't think we have enough information to accurately compare civilization progress between planets with or without a Gods-War. How long did life exist on both worlds? Was there any other technology diffusion from other worlds? Etc.
Now for some historical nerd stuff - don't take it personally, as this is not popular knowledge and most of this time period is skimmed over in schools. I believe in authors creative vision and fantasy is absolutely the place to divergent from history or science or both

- but fans should be aware and not take it as some historically accurate game. So yeah the arguments that X should or shouldn't be in game because of history are straight up wrong. It’s more about what the devs want to add
CoC2 is one of the most anachronistic fantasy worlds I've seen. There is very little historical Bronze Age here. A few good examples: Vitruvius, for whom Balak did research and it shows; advanced waterworks (yes, they are ancient despite popular belief); and the Minoans, but the name as they were a legitimate Bronze Age civilization otherwise in game they are Romans. Everything else is from other periods, just slapped with bronze as a "worse" metal than iron, which in reality is not true.
The whole idea that a "Gods-War" would regress civilization is flawed because it is the exact opposite of what happened in our history: a huge civilization upheaval (the Bronze Age Collapse) forced people around the Mediterranean to adopt iron. The "iron is progress" idea is one that holds only if you know about steel (around 2,000 years after the collapse) and our general historical trajectory. But from the POV of a person during the collapse, it was a fight for survival and using a worse alternative (yes, worse). Early iron production was decentralized, which was a big reason why it stuck and would be really difficult to "forget" or "lose". Technologies that are lost are the ones connected with luxury or secrets, not basic survival.
Above is only true for Middle East, Egypt and Greece - China had a lot less dramatic transition. In reality civilization on Earth, at certain point, NEEDS to use Iron - because of it abundance and rarity of other materials.
For weapons, there were swords that we today call Bronze Age "rapiers" - thrusting bronze swords that were, of course, a lot shorter than anything from the 16th century onwards.
Here, the additional problem is naming. The names of weapons and classifications used today are modern inventions; in reality, all weapons were handmade and would differ from one to another. What we call a "short sword" today, for example, the Roman gladius, would have just been a gladius so, just a "sword" to a Roman. Similarly with rapiers, in Italy they were just called "spada", which again just means "sword". This is despite "rapier" being a period English term, which shows the complete lack of standardization in historical periods. Not to mention, even English rapiers evolved, starting as cut-and-thrust weapons and ending as blades with which you could barely cut. The line between a sword and rapier was blurry and sometimes more based on usage than characteristics.
Bronze age is quite the underestimate period of our history. Bronze Age civilization built the pyramids (2560 BC), and it took almost 4,000 years before humanity constructed another building of comparable height - the Lincoln Cathedral in England (tall spire added in 1311), which later collapsed not long after its completion. After that, the next major leap was the Eiffel Tower (1889). Note - ofc building a tall structure is just but a one piece of overall technological level.
Some examples of bronze age weapon and armour.
Sword is from Britain and is 60cm long (photo is is quite zoomed) dated c.1400-1275 B.C
Dendra panoply Greece dated 1500 B.C